Any integer n can be expressed as a sum of kth powers. You might know the most famous example, 1729, which can be expressed as a sum of two cubes in two different ways, 10^3 + 9^3 and 12^3 + 1^3. It can also be expressed as 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + 1^3 + ... + 1^3, that is, 1^3 added up 1729 times. On this page, solutions like that will be abbreviated in the form x(y^z), so our example would be 1729(1^3).
For some integers, n(1^k) is the only available solution, specifically, for all n < 2^k. For all others, a solution of much fewer kth powers than n is available. In the table below, I've tried to find the solution using the fewest powers. Solutions of the form n(1^k) are implied when a given cell is blank. In the draft version, some cells will show things like "^3 + ^3" because I haven't gotten around to filling them in.
| n | Σx^2 | Σx^3 | Σx^4 | Σx^5 | Σx^6 | Σx^7 | Σx^8 |
|---|---|---|---|---|---|---|---|
| 4 | 2^2 | ||||||
| 5 | 2^2 + 1^2 | ||||||
| 6 | 2^2 + 2(1^2) | ||||||
| 7 | 2^2 + 3(1^2) | ||||||
| 8 | 2(2^2) | 2^3 | |||||
| 9 | 3^2 | 2^3 + 1^3 | |||||
| 10 | 3^2 + 1^2 | 2^3 + 2(1^3) | |||||
| 11 | 3^2 + 2(1^2) | 2^3 + 3(1^3) | |||||
| 12 | 3(2^2) | 2^3 + 4(1^3) | |||||
| 13 | 3^2 + 2^2 | 2^3 + 5(1^3) | |||||
| 14 | 3^2 + 2^2 + 1^2 | 2^3 + 6(1^3) | |||||
| 15 | 3^2 + 2^2 + 2(1^2) | 2^3 + 7(1^3) | |||||
| 16 | 4^2 | 2(2^3) | 2^4 | ||||
| 17 | 4^2 + 1^2 | 2(2^3) + 1^3 | 2^4 + 1^4 | ||||
| 18 | 2(3^2) | 2(2^3) + 2(1^3) | 2^4 + 2(1^4) | ||||
| 19 | 2(3^2) + 1^2 | 2(2^3) + 3(1^3) | 2^4 + 3(1^4) | ||||
| 20 | 4^2 + 2^2 | 2(2^3) + 4(1^3) | 2^4 + 4(1^4) | ||||
| 21 | 4^2 + 2^2 + 1^2 | 2(2^3) + 5(1^3) | 2^4 + 5(1^4) | ||||
| 22 | 2(3^2) + 2^2 | 2(2^3) + 6(1^3) | 2^4 + 6(1^4) | ||||
| 23 | 2(3^2) + 2^2 + 1^2 | 2(2^3) + 7(1^3) | 2^4 + 7(1^4) | ||||
| 24 | 4^2 + 2(2^2) | 3(2^3) | 2^4 + 8(1^4) | ||||
| 25 | 5^2 | 3(2^3) + 1^3 | 2^4 + 9(1^4) | ||||
| 26 | 5^2 + 1^2 | 3(2^3) + 2(1^3) | 2^4 + 10(1^4) | ||||
| 27 | 5^2 + 2(1^2) | 3^3 | 2^4 + 11(1^4) | ||||
| 28 | 5^2 + 3(1^2) | 3^3 + 1^3 | 2^4 + 12(1^4) | ||||
| 29 | 5^2 + 2^2 | 3^3 + 2(1^3) | 2^4 + 13(1^4) | ||||
| 30 | 5^2 + 2^2 + 1^2 | 3^3 + 3(1^3) | 2^4 + 14(1^4) | ||||
| 31 | 5^2 + 2^2 + 2(1^2) | 3^3 + 4(1^3) | 2^4 + 15(1^4) | ||||
| 32 | 2(4^2) | 4(2^3) | 2(2^4) | 2^5 | |||
| 33 | 2(4^2) + 1^2 | 4(2^3) + 1^3 | 2(2^4) + 1^4 | 2^5 + 1^5 | |||
| 34 | 5^2 + 3^2 | 4(2^3) + 2(1^3) | 2(2^4) + 2(1^4) | 2^5 + 2(1^5) | |||
| 35 | 5^2 + 3^2 + 1^2 | 3^3 + 2^3 | 2(2^4) + 3(1^4) | 2^5 + 3(1^5) | |||
| 36 | 6^2 | 3^3 + 2^3 + 1^3 | 2(2^4) + 4(1^4) | 2^5 + 4(1^5) | |||
| 37 | 6^2 + 1^2 | 3^3 + 2^3 + 2(1^3) | 2(2^4) + 5(1^4) | 2^5 + 5(1^5) | |||
| 38 | 5^2 + 3^2 + 2^2 | 3^3 + 2^3 + 3(1^3) | 2(2^4) + 6(1^4) | 2^5 + 6(1^5) | |||
| 39 | 5^2 + 3^2 + 2^2 + 1^2 | 3^3 + 2^3 + 4(1^3) | 2(2^4) + 7(1^4) | 2^5 + 7(1^5) | |||
| 40 | 6^2 + 2^2 | 5(2^3) | 2(2^4) + 8(1^4) | 2^5 + 8(1^5) | |||
| 41 | 5^2 + 4^2 | 5(2^3) + 1^3 | 2(2^4) + 9(1^4) | 2^5 + 9(1^5) | |||
| 42 | 5^2 + 4^2 + 1^2 | 5(2^3) + 2(1^3) | 2(2^4) + 10(1^4) | 2^5 + 10(1^5) | |||
| 43 | 5^2 + 2(3^2) | 3^3 + 2(2^3) | 2(2^4) + 11(1^4) | 2^5 + 11(1^5) | |||
| 44 | 6^2 + 2(2^2) | 3^3 + 2(2^3) + 1^3 | 2(2^4) + 12(1^4) | 2^5 + 12(1^5) | |||
| 45 | 6^2 + 3^2 | 3^3 + 2(2^3) + 2(1^3) | 2(2^4) + 13(1^4) | 2^5 + 13(1^5) | |||
| 46 | 6^2 + 3^2 + 1^2 | 3^3 + 2(2^3) + 3(1^3) | 2(2^4) + 14(1^4) | 2^5 + 14(1^5) | |||
| 47 | 6^2 + 3^2 + 2(1^2) | 3^3 + 2(2^3) + 4(1^3) | 2(2^4) + 15(1^4) | 2^5 + 15(1^5) | |||
| 48 | 3(4^2) | 6(2^3) | 3(2^4) | 2^5 + 16(1^5) | |||
| 49 | 7^2 | 6(2^3) + 1^3 | 3(2^4) + 1^4 | 2^5 + 17(1^5) | |||
| 50 | 2(5^2) | 6(2^3) + 2(1^3) | 3(2^4) + 2(1^4) | 2^5 + 18(1^5) | |||
| 51 | 7^2 + 2(1^2) | 3^3 + 3(2^3) | 3(2^4) + 3(1^4) | 2^5 + 19(1^5) | |||
| 52 | 6^2 + 4^2 | 3^3 + 3(2^3) + 1^3 | 3(2^4) + 4(1^4) | 2^5 + 20(1^5) | |||
| 53 | 7^2 + 2^2 | 3^3 + 3(2^3) + 2(1^3) | 3(2^4) + 5(1^4) | 2^5 + 21(1^5) | |||
| 54 | 6^2 + 2(3^2) | 2(3^3) | 3(2^4) + 6(1^4) | 2^5 + 22(1^5) | |||
| 55 | 7^2 + 2^2 + 2(1^2) | 2(3^3) + 1^3 | 3(2^4) + 7(1^4) | 2^5 + 23(1^5) | |||
| 56 | 6^2 + 4^2 + 2^2 | 7(2^3) | 3(2^4) + 8(1^4) | 2^5 + 24(1^5) | |||
| 57 | 7^2 + 2(2^2) | 2(3^3) + 3(1^3) | 3(2^4) + 9(1^4) | 2^5 + 25(1^5) | |||
| 58 | 7^2 + 3^2 | 2(3^3) + 4(1^3) | 3(2^4) + 10(1^4) | 2^5 + 26(1^5) | |||
| 59 | 2(5^2) + 3^2 | 2(3^3) + 5(1^3) | 3(2^4) + 11(1^4) | 2^5 + 27(1^5) | |||
| 60 | 2(5^2) + 3^2 + 1^2 | 2(3^3) + 6(1^3) | 3(2^4) + 12(1^4) | 2^5 + 28(1^5) | |||
| 61 | 6^2 + 5^2 | 3^3 + 4(2^3) + 2(1^3) | 3(2^4) + 13(1^4) | 2^5 + 29(1^5) | |||
| 62 | 7^2 + 3^2 + 2^2 | 2(3^3) + 2^3 | 3(2^4) + 14(1^4) | 2^5 + 30(1^5) | |||
| 63 | 6^2 + 3(3^2) | 2(3^3) + 2^3 + 1^3 | 3(2^4) + 15(1^4) | 2^5 + 31(1^5) | |||
| 64 | 8^2 | 4^3 | 4(2^4) | 2(2^5) | 2^6 | ||
| 65 | 7^2 + 4^2 | 4^3 + 1^3 | 4(2^4) | 2(2^5) + 1^5 | 2^6 + 1^6 | ||
| 66 | 2(5^2) + 4^2 | 4^3 + 2(1^3) | 4(2^4) + 2(1^4) | 2(2^5) + 2(1^5) | 2^6 + 2(1^6) | ||
| 67 | 7^2 + 2(3^2) | 4^3 + 3(1^3) | 4(2^4) + 3(1^4) | 2(2^5) + 3(1^5) | 2^6 + 3(1^6) | ||
| 68 | 8^2 + 2^2 | 4^3 + 4(1^3) | 4(2^4) + 4(1^4) | 2(2^5) + 4(1^5) | 2^6 + 4(1^6) | ||
| 69 | 7^2 + 4^2 + 2^2 | 4^3 + 5(1^3) | 4(2^4) + 5(1^4) | 2(2^5) + 5(1^5) | 2^6 + 5(1^6) | ||
| 70 | 6^2 + 5^2 + 3^2 | 2(3^3) + 2(2^3) | 4(2^4) + 6(1^4) | 2(2^5) + 6(1^5) | 2^6 + 6(1^6) | ||
| 71 | 6^2 + 5^2 + 3^2 + 1^2 | 2(3^3) + 2(2^3) + 1^3 | 4(2^4) + 7(1^4) | 2(2^5) + 7(1^5) | 2^6 + 7(1^6) | ||
| 72 | 2(6^2) | 4^3 + 2^3 | 4(2^4) + 8(1^4) | 2(2^5) + 8(1^5) | 2^6 + 8(1^6) | ||
| 73 | 8^2 + 3^2 | 4^3 + 2^3 + 1^3 | 4(2^4) + 9(1^4) | 2(2^5) + 9(1^5) | 2^6 + 9(1^6) | ||
| 74 | 7^2 + 5^2 | 4^3 + 2^3 + 2(1^3) | 4(2^4) + 10(1^4) | 2(2^5) + 10(1^5) | 2^6 + 10(1^6) | ||
| 75 | 3(5^2) | 4^3 + 2^3 + 3(1^3) | 4(2^4) + 11(1^4) | 2(2^5) + 11(1^5) | 2^6 + 11(1^6) | ||
| 76 | 2(6^2) + 2^2 | 4^3 + 2^3 + 4(1^3) | 4(2^4) + 12(1^4) | 2(2^5) + 12(1^5) | 2^6 + 12(1^6) | ||
| 77 | 8^2 + 3^2 + 2^2 | 4^3 + 2^3 + 5(1^3) | 4(2^4) + 13(1^4) | 2(2^5) + 13(1^5) | 2^6 + 13(1^6) | ||
| 78 | 7^2 + 5^2 + 2^2 | 2(3^3) + 3(2^3) | 4(2^4) + 14(1^4) | 2(2^5) + 14(1^5) | 2^6 + 14(1^6) | ||
| 79 | 7^2 + 5^2 + 2^2 + 1^2 | 2(3^3) + 3(2^3) + 1^3 | 4(2^4) + 15(1^4) | 2(2^5) + 15(1^5) | 2^6 + 15(1^6) | ||
| 80 | 8^2 + 4^2 | 4^3 + 2(2^3) | 5(2^4) | 2(2^5) + 16(1^5) | 2^6 + 16(1^6) | ||
| 81 | 9^2 | 3(3^3) | 3^4 | 2(2^5) + 17(1^5) | 2^6 + 17(1^6) | ||
| 82 | 9^2 + 1^2 | 3(3^3) + 1^3 | 3^4 + 1^4 | 2(2^5) + 18(1^5) | 2^6 + 18(1^6) | ||
| 83 | 7^2 + 5^2 + 3^2 | 3(3^3) + 2(1^3) | 3^4 + 2(1^4) | 2(2^5) + 19(1^5) | 2^6 + 19(1^6) | ||
| 84 | 8^2 + 4^2 + 2^2 | 3(3^3) + 3(1^3) | 3^4 + 3(1^4) | 2(2^5) + 20(1^5) | 2^6 + 20(1^6) | ||
| 85 | 9^2 + 2^2 | 3(3^3) + 4(1^3) | 3^4 + 4(1^4) | 2(2^5) + 21(1^5) | 2^6 + 21(1^6) | ||
| 86 | 6^2 + 2(5^2) | 3(3^3) + 5(1^3) | 3^4 + 5(1^4) | 2(2^5) + 22(1^5) | 2^6 + 22(1^6) | ||
| 87 | 7^2 + 5^2 + 3^2 + 2^2 | 2(3^3) + 4(2^3) + 1^3 | 3^4 + 6(1^4) | 2(2^5) + 23(1^5) | 2^6 + 23(1^6) | ||
| 88 | 2(6^2) + 4^2 | 4^3 + 3(2^3) | 3^4 + 7(1^4) | 2(2^5) + 24(1^5) | 2^6 + 24(1^6) | ||
| 89 | 8^2 + 5^2 | 3(3^3) + 2^3 | 3^4 + 8(1^4) | 2(2^5) + 25(1^5) | 2^6 + 25(1^6) | ||
| 90 | 9^2 + 3^2 | 3(3^3) + 2^3 + 1^3 | 3^4 + 9(1^4) | 2(2^5) + 26(1^5) | 2^6 + 26(1^6) | ||
| 91 | 9^2 + 3^2 + 1^2 | 4^3 + 3^3 | 3^4 + 10(1^4) | 2(2^5) + 27(1^5) | 2^6 + 27(1^6) | ||
| 92 | 2(6^2) + 4^2 + 2^2 | 4^3 + 3^3 + 1^3 | 3^4 + 11(1^4) | 2(2^5) + 28(1^5) | 2^6 + 28(1^6) | ||
| 93 | 8^2 + 5^2 + 2^2 | 4^3 + 3^3 + 2(1^3) | 3^4 + 12(1^4) | 2(2^5) + 29(1^5) | 2^6 + 29(1^6) | ||
| 94 | 9^2 + 3^2 + 2^2 | 4^3 + 3^3 + 3(1^3) | 3^4 + 13(1^4) | 2(2^5) + 30(1^5) | 2^6 + 30(1^6) | ||
| 95 | 9^2 + 3^2 + 2^2 + 1^2 | 4^3 + 3^3 + 4(1^3) | 3^4 + 14(1^4) | 2(2^5) + 31(1^5) | 2^6 + 31(1^6) | ||
| 96 | 8^2 + 2(4^2) | 4^3 + 4(2^3) | 6(2^4) | 3(2^5) | 2^6 + 32(1^6) | ||
| 97 | 9^2 + 4^2 | 4^3 + 4(2^3) + 1^3 | 3^4 + 2^4 | 3(2^5) + 1^5 | 2^6 + 33(1^6) | ||
| 98 | 2(7^2) | 4^3 + 4(2^3) + 2(1^3) | 6(2^4) + 2(1^4) | 3(2^5) + 2(1^5) | 2^6 + 34(1^6) | ||
| 99 | 2(7^2) + 1^2 | 4^3 + 3^3 + 2^3 | 6(2^4) + 3(1^4) | 3(2^5) + 3(1^5) | 2^6 + 35(1^6) | ||
| 100 | 10^2 | 4^3 + 3^3 + 2^3 + 1^3 | 6(2^4) + 4(1^4) | 3(2^5) + 4(1^5) | 2^6 + 36(1^6) | ||
| 101 | 10^2 + 1^2 | 4^3 + 3^3 + 2^3 + 2(1^3) | 6(2^4) + 5(1^4) | 3(2^5) + 5(1^5) | 2^6 + 37(1^6) | ||
| 102 | 2(7^2) + 2^2 | 4^3 + 3^3 + 2^3 + 3(1^3) | 6(2^4) + 6(1^4) | 3(2^5) + 6(1^5) | 2^6 + 38(1^6) | ||
| 103 | 2(7^2) + 2^2 + 1^2 | 4^3 + 3^3 + 2^3 + 4(1^3) | 6(2^4) + 7(1^4) | 3(2^5) + 7(1^5) | 2^6 + 39(1^6) | ||
| 104 | 10^2 + 2^2 | 4^3 + 5(2^3) | 6(2^4) + 8(1^4) | 3(2^5) + 8(1^5) | 2^6 + 40(1^6) | ||
| 105 | 8^2 + 5^2 + 4^2 | 3(3^3) + 3(2^3) | 3^4 + 2^4 + 8(1^4) | 3(2^5) + 9(1^5) | 2^6 + 41(1^6) | ||
| 106 | 9^2 + 5^2 | 3(3^3) + 3(2^3) + 1^3 | 3^4 + 2^4 + 9(1^4) | 3(2^5) + 10(1^5) | 2^6 + 42(1^6) | ||
| 107 | 2(7^2) + 3^2 | 3(3^3) + 3(2^3) + 2(1^3) | 3^4 + 2^4 + 10(1^4) | 3(2^5) + 11(1^5) | 2^6 + 43(1^6) | ||
| 108 | 10^2 + 2(2^2) | 4(3^3) | 3^4 + 2^4 + 11(1^4) | 3(2^5) + 12(1^5) | 2^6 + 44(1^6) | ||
| 109 | 10^2 + 3^2 | 4(3^3) + 1^3 | 3^4 + 2^4 + 12(1^4) | 3(2^5) + 13(1^5) | 2^6 + 45(1^6) | ||
| 110 | 9^2 + 5^2 + 2^2 | 4(3^3) + 2(1^3) | 3^4 + 2^4 + 13(1^4) | 3(2^5) + 14(1^5) | 2^6 + 46(1^6) | ||
| 111 | 6^2 + 3(5^2) | 4(3^3) + 3(1^3) | 3^4 + 2^4 + 14(1^4) | 3(2^5) + 15(1^5) | 2^6 + 47(1^6) | ||
| 112 | 10^2 + 3(2^2) | 4^3 + 6(2^3) | 7(2^4) | 3(2^5) + 16(1^5) | 2^6 + 48(1^6) | ||
| 113 | 8^2 + 7^2 | 4^3 + 6(2^3) + 1^3 | 3^4 + 2(2^4) | 3(2^5) + 17(1^5) | 2^6 + 49(1^6) | ||
| 114 | 8^2 + 2(5^2) | 3(3^3) + 4(2^3) + 1^3 | 3^4 + 2(2^4) + 1^4 | 3(2^5) + 18(1^5) | 2^6 + 50(1^6) | ||
| 115 | 9^2 + 5^2 + 3^2 | 4^3 + 3^3 + 3(2^3) | 3^4 + 2(2^4) + 2(1^4) | 3(2^5) + 19(1^5) | 2^6 + 51(1^6) | ||
| 116 | 10^2 + 4^2 | 4^3 + 3^3 + 3(2^3) + 1^3 | 3^4 + 2(2^4) + 3(1^4) | 3(2^5) + 20(1^5) | 2^6 + 52(1^6) | ||
| 117 | 9^2 + 6^2 | 4^3 + 3^3 + 3(2^3) + 2(1^3) | 3^4 + 2(2^4) + 4(1^4) | 3(2^5) + 21(1^5) | 2^6 + 53(1^6) | ||
| 118 | 9^2 + 6^2 + 1^2 | 4^3 + 2(3^3) | 3^4 + 2(2^4) + 5(1^4) | 3(2^5) + 22(1^5) | 2^6 + 54(1^6) | ||
| 119 | 7^2 + 6^2 + 5^2 + 3^2 | 4^3 + 2(3^3) + 1^3 | 3^4 + 2(2^4) + 6(1^4) | 3(2^5) + 23(1^5) | 2^6 + 55(1^6) | ||
| 120 | 10^2 + 4^2 + 2^2 | 4^3 + 7(2^3) | 3^4 + 2(2^4) + 7(1^4) | 3(2^5) + 24(1^5) | 2^6 + 56(1^6) | ||
| 121 | 11^2 | 4^3 + 2(3^3) + 3(1^3) | 3^4 + 2(2^4) + 8(1^4) | 3(2^5) + 25(1^5) | 2^6 + 57(1^6) | ||
| 122 | 11^2 + 1^2 | 4^3 + 2(3^3) + 4(1^3) | 3^4 + 2(2^4) + 9(1^4) | 3(2^5) + 26(1^5) | 2^6 + 58(1^6) | ||
| 123 | 2(7^2) + 5^2 | 4^3 + 2(3^3) + 5(1^3) | 3^4 + 2(2^4) + 10(1^4) | 3(2^5) + 27(1^5) | 2^6 + 59(1^6) | ||
| 124 | 2(7^2) + 5^2 + 1^2 | 4(3^3) + 2(2^3) | 3^4 + 2(2^4) + 11(1^4) | 3(2^5) + 28(1^5) | 2^6 + 60(1^6) | ||
| 125 | 11^2 + 2^2 | 5^3 | 3^4 + 2(2^4) + 12(1^4) | 3(2^5) + 29(1^5) | 2^6 + 61(1^6) | ||
| 126 | 9^2 + 6^2 + 3^2 | 5^3 + 1^3 | 3^4 + 2(2^4) + 13(1^4) | 3(2^5) + 30(1^5) | 2^6 + 62(1^6) | ||
| 127 | 9^2 + 6^2 + 3^2 + 1^2 | 5^3 + 2(1^3) | 3^4 + 2(2^4) + 14(1^4) | 3(2^5) + 31(1^5) | 2^6 + 63(1^6) | ||
| 128 | 2(8^2) | 2(4^3) | 8(2^4) | 4(2^5) | 2(2^6) | 2^7 | |
| 129 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 1^5 | 2(2^6) + 1^6 | 2^7 + 1^7 | |
| 130 | 9^2 + 7^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 2(1^5) | 2(2^6) + 2(1^6) | 2^7 + 2(1^7) | |
| 131 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 3(1^5) | 2(2^6) + 3(1^6) | 2^7 + 3(1^7) | |
| 132 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 4(1^5) | 2(2^6) + 4(1^6) | 2^7 + 4(1^7) | |
| 133 | ^2 + ^2 | 5^3 + 2^3 | ^4 + ^4 | 4(2^5) + 5(1^5) | 2(2^6) + 5(1^6) | 2^7 + 5(1^7) | |
| 134 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 6(1^5) | 2(2^6) + 6(1^6) | 2^7 + 6(1^7) | |
| 135 | ^2 + ^2 | 5(3^3) | ^4 + ^4 | 4(2^5) + 7(1^5) | 2(2^6) + 7(1^6) | 2^7 + 7(1^7) | |
| 136 | 10^2 + 6^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 8(1^5) | 2(2^6) + 8(1^6) | 2^7 + 8(1^7) | |
| 137 | 11^2 + 4^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 9(1^5) | 2(2^6) + 9(1^6) | 2^7 + 9(1^7) | |
| 138 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 10(1^5) | 2(2^6) + 10(1^6) | 2^7 + 10(1^7) | |
| 139 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 11(1^5) | 2(2^6) + 11(1^6) | 2^7 + 11(1^7) | |
| 140 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 12(1^5) | 2(2^6) + 12(1^6) | 2^7 + 12(1^7) | |
| 141 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 13(1^5) | 2(2^6) + 13(1^6) | 2^7 + 13(1^7) | |
| 142 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 14(1^5) | 2(2^6) + 14(1^6) | 2^7 + 14(1^7) | |
| 143 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 15(1^5) | 2(2^6) + 15(1^6) | 2^7 + 15(1^7) | |
| 144 | 12^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 16(1^5) | 2(2^6) + 16(1^6) | 2^7 + 16(1^7) | |
| 145 | 9^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 17(1^5) | 2(2^6) + 17(1^6) | 2^7 + 17(1^7) | |
| 146 | 11^2 + 5^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 18(1^5) | 2(2^6) + 18(1^6) | 2^7 + 18(1^7) | |
| 147 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 19(1^5) | 2(2^6) + 19(1^6) | 2^7 + 19(1^7) | |
| 148 | 12^2 + 2^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 20(1^5) | 2(2^6) + 20(1^6) | 2^7 + 20(1^7) | |
| 149 | 10^2 + 7^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 21(1^5) | 2(2^6) + 21(1^6) | 2^7 + 21(1^7) | |
| 150 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 22(1^5) | 2(2^6) + 22(1^6) | 2^7 + 22(1^7) | |
| 151 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 23(1^5) | 2(2^6) + 23(1^6) | 2^7 + 23(1^7) | |
| 152 | ^2 + ^2 | 5^3 + 3^3 | ^4 + ^4 | 4(2^5) + 24(1^5) | 2(2^6) + 24(1^6) | 2^7 + 24(1^7) | |
| 153 | 12^2 + 3^2 | 1^3 + 5^3 + 3^3 | ^4 + ^4 | 4(2^5) + 25(1^5) | 2(2^6) + 25(1^6) | 2^7 + 25(1^7) | |
| 154 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 26(1^5) | 2(2^6) + 26(1^6) | 2^7 + 26(1^7) | |
| 155 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 27(1^5) | 2(2^6) + 27(1^6) | 2^7 + 27(1^7) | |
| 156 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 28(1^5) | 2(2^6) + 28(1^6) | 2^7 + 28(1^7) | |
| 157 | 11^2 + 6^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 29(1^5) | 2(2^6) + 29(1^6) | 2^7 + 29(1^7) | |
| 158 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 30(1^5) | 2(2^6) + 30(1^6) | 2^7 + 30(1^7) | |
| 159 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 4(2^5) + 31(1^5) | 2(2^6) + 31(1^6) | 2^7 + 31(1^7) | |
| 160 | 12^2 + 4^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) | 2(2^6) + 32(1^6) | 2^7 + 32(1^7) | |
| 161 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 1^5 | 2(2^6) + 33(1^6) | 2^7 + 33(1^7) | |
| 162 | 2(9^2) | 6(3^3) | 2(3^4) | 5(2^5) + 2(1^5) | 2(2^6) + 34(1^6) | 2^7 + 34(1^7) | |
| 163 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 3(1^5) | 2(2^6) + 35(1^6) | 2^7 + 35(1^7) | |
| 164 | 10^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 4(1^5) | 2(2^6) + 36(1^6) | 2^7 + 36(1^7) | |
| 165 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 5(1^5) | 2(2^6) + 37(1^6) | 2^7 + 37(1^7) | |
| 166 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 6(1^5) | 2(2^6) + 38(1^6) | 2^7 + 38(1^7) | |
| 167 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 7(1^5) | 2(2^6) + 39(1^6) | 2^7 + 39(1^7) | |
| 168 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 8(1^5) | 2(2^6) + 40(1^6) | 2^7 + 40(1^7) | |
| 169 | 13^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 9(1^5) | 2(2^6) + 41(1^6) | 2^7 + 41(1^7) | |
| 170 | 11^2 + 7^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 10(1^5) | 2(2^6) + 42(1^6) | 2^7 + 42(1^7) | |
| 171 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 11(1^5) | 2(2^6) + 43(1^6) | 2^7 + 43(1^7) | |
| 172 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 12(1^5) | 2(2^6) + 44(1^6) | 2^7 + 44(1^7) | |
| 173 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 13(1^5) | 2(2^6) + 45(1^6) | 2^7 + 45(1^7) | |
| 174 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 14(1^5) | 2(2^6) + 46(1^6) | 2^7 + 46(1^7) | |
| 175 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 15(1^5) | 2(2^6) + 47(1^6) | 2^7 + 47(1^7) | |
| 176 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 16(1^5) | 2(2^6) + 48(1^6) | 2^7 + 48(1^7) | |
| 177 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 17(1^5) | 2(2^6) + 49(1^6) | 2^7 + 49(1^7) | |
| 178 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 18(1^5) | 2(2^6) + 50(1^6) | 2^7 + 50(1^7) | |
| 179 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 19(1^5) | 2(2^6) + 51(1^6) | 2^7 + 51(1^7) | |
| 180 | 12^2 + 6^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 20(1^5) | 2(2^6) + 52(1^6) | 2^7 + 52(1^7) | |
| 181 | 10^2 + 9^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 21(1^5) | 2(2^6) + 53(1^6) | 2^7 + 53(1^7) | |
| 182 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 22(1^5) | 2(2^6) + 54(1^6) | 2^7 + 54(1^7) | |
| 183 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 23(1^5) | 2(2^6) + 55(1^6) | 2^7 + 55(1^7) | |
| 184 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 24(1^5) | 2(2^6) + 56(1^6) | 2^7 + 56(1^7) | |
| 185 | 11^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 25(1^5) | 2(2^6) + 57(1^6) | 2^7 + 57(1^7) | |
| 186 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 26(1^5) | 2(2^6) + 58(1^6) | 2^7 + 58(1^7) | |
| 187 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 27(1^5) | 2(2^6) + 59(1^6) | 2^7 + 59(1^7) | |
| 188 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 28(1^5) | 2(2^6) + 60(1^6) | 2^7 + 60(1^7) | |
| 189 | ^2 + ^2 | 5^3 + 4^3 | ^4 + ^4 | 5(2^5) + 29(1^5) | 2(2^6) + 61(1^6) | 2^7 + 61(1^7) | |
| 190 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 30(1^5) | 2(2^6) + 62(1^6) | 2^7 + 62(1^7) | |
| 191 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 5(2^5) + 31(1^5) | 2(2^6) + 63(1^6) | 2^7 + 63(1^7) | |
| 192 | ^2 + ^2 | 3(4^3) | ^4 + ^4 | 6(2^5) | 3(2^6) | 2^7 + 64(1^7) | |
| 193 | 12^2 + 7^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 1^5 | 3(2^6) + 1^6 | 2^7 + 65(1^7) | |
| 194 | 14^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 2(1^5) | 3(2^6) + 2(1^6) | 2^7 + 66(1^7) | |
| 195 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 3(1^5) | 3(2^6) + 3(1^6) | 2^7 + 67(1^7) | |
| 196 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 4(1^5) | 3(2^6) + 4(1^6) | 2^7 + 68(1^7) | |
| 197 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 5(1^5) | 3(2^6) + 5(1^6) | 2^7 + 69(1^7) | |
| 198 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 6(1^5) | 3(2^6) + 6(1^6) | 2^7 + 70(1^7) | |
| 199 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 7(1^5) | 3(2^6) + 7(1^6) | 2^7 + 71(1^7) | |
| 200 | 14^2 + 2^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 8(1^5) | 3(2^6) + 8(1^6) | 2^7 + 72(1^7) | |
| 201 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 9(1^5) | 3(2^6) + 9(1^6) | 2^7 + 73(1^7) | |
| 202 | 11^2 + 9^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 10(1^5) | 3(2^6) + 10(1^6) | 2^7 + 74(1^7) | |
| 203 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 11(1^5) | 3(2^6) + 11(1^6) | 2^7 + 75(1^7) | |
| 204 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 12(1^5) | 3(2^6) + 12(1^6) | 2^7 + 76(1^7) | |
| 205 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 13(1^5) | 3(2^6) + 13(1^6) | 2^7 + 77(1^7) | |
| 206 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 14(1^5) | 3(2^6) + 14(1^6) | 2^7 + 78(1^7) | |
| 207 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 15(1^5) | 3(2^6) + 15(1^6) | 2^7 + 79(1^7) | |
| 208 | 12^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 16(1^5) | 3(2^6) + 16(1^6) | 2^7 + 80(1^7) | |
| 209 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 17(1^5) | 3(2^6) + 17(1^6) | 2^7 + 81(1^7) | |
| 210 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 18(1^5) | 3(2^6) + 18(1^6) | 2^7 + 82(1^7) | |
| 211 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 19(1^5) | 3(2^6) + 19(1^6) | 2^7 + 83(1^7) | |
| 212 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 20(1^5) | 3(2^6) + 20(1^6) | 2^7 + 84(1^7) | |
| 213 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 21(1^5) | 3(2^6) + 21(1^6) | 2^7 + 85(1^7) | |
| 214 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 22(1^5) | 3(2^6) + 22(1^6) | 2^7 + 86(1^7) | |
| 215 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 23(1^5) | 3(2^6) + 23(1^6) | 2^7 + 87(1^7) | |
| 216 | ^2 + ^2 | 6^3 | ^4 + ^4 | 6(2^5) + 24(1^5) | 3(2^6) + 24(1^6) | 2^7 + 88(1^7) | |
| 217 | ^2 + ^2 | 6^3 + 1^3 | ^4 + ^4 | 6(2^5) + 25(1^5) | 3(2^6) + 25(1^6) | 2^7 + 89(1^7) | |
| 218 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 26(1^5) | 3(2^6) + 26(1^6) | 2^7 + 90(1^7) | |
| 219 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 27(1^5) | 3(2^6) + 27(1^6) | 2^7 + 91(1^7) | |
| 220 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 28(1^5) | 3(2^6) + 28(1^6) | 2^7 + 92(1^7) | |
| 221 | 11^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 29(1^5) | 3(2^6) + 29(1^6) | 2^7 + 93(1^7) | |
| 222 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 30(1^5) | 3(2^6) + 30(1^6) | 2^7 + 94(1^7) | |
| 223 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 6(2^5) + 31(1^5) | 3(2^6) + 31(1^6) | 2^7 + 95(1^7) | |
| 224 | ^2 + ^2 | 6^3 + 2^3 | ^4 + ^4 | 7(2^5) | 3(2^6) + 32(1^6) | 2^7 + 96(1^7) | |
| 225 | 15^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 1^5 | 3(2^6) + 33(1^6) | 2^7 + 97(1^7) | |
| 226 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 2(1^5) | 3(2^6) + 34(1^6) | 2^7 + 98(1^7) | |
| 227 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 3(1^5) | 3(2^6) + 35(1^6) | 2^7 + 99(1^7) | |
| 228 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 4(1^5) | 3(2^6) + 36(1^6) | 2^7 + 100(1^7) | |
| 229 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 5(1^5) | 3(2^6) + 37(1^6) | 2^7 + 101(1^7) | |
| 230 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 6(1^5) | 3(2^6) + 38(1^6) | 2^7 + 102(1^7) | |
| 231 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 7(1^5) | 3(2^6) + 39(1^6) | 2^7 + 103(1^7) | |
| 232 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 8(1^5) | 3(2^6) + 40(1^6) | 2^7 + 104(1^7) | |
| 233 | 13^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 9(1^5) | 3(2^6) + 41(1^6) | 2^7 + 105(1^7) | |
| 234 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 10(1^5) | 3(2^6) + 42(1^6) | 2^7 + 106(1^7) | |
| 235 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 11(1^5) | 3(2^6) + 43(1^6) | 2^7 + 107(1^7) | |
| 236 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 12(1^5) | 3(2^6) + 44(1^6) | 2^7 + 108(1^7) | |
| 237 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 13(1^5) | 3(2^6) + 45(1^6) | 2^7 + 109(1^7) | |
| 238 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 14(1^5) | 3(2^6) + 46(1^6) | 2^7 + 110(1^7) | |
| 239 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 15(1^5) | 3(2^6) + 47(1^6) | 2^7 + 111(1^7) | |
| 240 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 16(1^5) | 3(2^6) + 48(1^6) | 2^7 + 112(1^7) | |
| 241 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 17(1^5) | 3(2^6) + 49(1^6) | 2^7 + 113(1^7) | |
| 242 | 2(11^2) | ^3 + ^3 | ^4 + ^4 | 7(2^5) + 18(1^5) | 3(2^6) + 50(1^6) | 2^7 + 114(1^7) | |
| 243 | ^2 + ^2 | 6^3 + 3^3 | ^4 + ^4 | 3^5 | 3(2^6) + 51(1^6) | 2^7 + 115(1^7) | |
| 244 | 12^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 1^5 | 3(2^6) + 52(1^6) | 2^7 + 116(1^7) | |
| 245 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 2(1^5) | 3(2^6) + 53(1^6) | 2^7 + 117(1^7) | |
| 246 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 3(1^5) | 3(2^6) + 54(1^6) | 2^7 + 118(1^7) | |
| 247 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 4(1^5) | 3(2^6) + 55(1^6) | 2^7 + 119(1^7) | |
| 248 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 5(1^5) | 3(2^6) + 56(1^6) | 2^7 + 120(1^7) | |
| 249 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 6(1^5) | 3(2^6) + 57(1^6) | 2^7 + 121(1^7) | |
| 250 | 13^2 + 9^2 | 2(5^3) | ^4 + ^4 | 3^5 + 7(1^5) | 3(2^6) + 58(1^6) | 2^7 + 122(1^7) | |
| 251 | ^2 + ^2 | 2(5^3) + 1^3 | ^4 + ^4 | 3^5 + 8(1^5) | 3(2^6) + 59(1^6) | 2^7 + 123(1^7) | |
| 252 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 9(1^5) | 3(2^6) + 60(1^6) | 2^7 + 124(1^7) | |
| 253 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 10(1^5) | 3(2^6) + 61(1^6) | 2^7 + 125(1^7) | |
| 254 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 11(1^5) | 3(2^6) + 62(1^6) | 2^7 + 126(1^7) | |
| 255 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 12(1^5) | 3(2^6) + 63(1^6) | 2^7 + 127(1^7) | |
| 256 | 16^2 | 4(4^3) | 4^4 | 8(2^5) | 4(2^6) | 2(2^7) | 2^8 |
| 257 | ^2 + ^2 | 4(4^3) + 1^3 | 4^4 + 1^4 | ^5 + ^5 | 4(2^6) + 1^6 | 2(2^7) + 1^7 | 2^8 + 1^8 |
| 258 | ^2 + ^2 | 2(5^3) + 2^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 2(1^6) | 2(2^7) + 2(1^7) | 2^8 + 2(1^8) |
| 259 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 3(1^6) | 2(2^7) + 3(1^7) | 2^8 + 3(1^8) |
| 260 | 14^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 4(1^6) | 2(2^7) + 4(1^7) | 2^8 + 4(1^8) |
| 261 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 5(1^6) | 2(2^7) + 5(1^7) | 2^8 + 5(1^8) |
| 262 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 6(1^6) | 2(2^7) + 6(1^7) | 2^8 + 6(1^8) |
| 263 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 7(1^6) | 2(2^7) + 7(1^7) | 2^8 + 7(1^8) |
| 264 | ^2 + ^2 | 4(4^3) + 2^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 8(1^6) | 2(2^7) + 8(1^7) | 2^8 + 8(1^8) |
| 265 | 12^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 9(1^6) | 2(2^7) + 9(1^7) | 2^8 + 9(1^8) |
| 266 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 10(1^6) | 2(2^7) + 10(1^7) | 2^8 + 10(1^8) |
| 267 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 11(1^6) | 2(2^7) + 11(1^7) | 2^8 + 11(1^8) |
| 268 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 12(1^6) | 2(2^7) + 12(1^7) | 2^8 + 12(1^8) |
| 269 | 13^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 13(1^6) | 2(2^7) + 13(1^7) | 2^8 + 13(1^8) |
| 270 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 14(1^6) | 2(2^7) + 14(1^7) | 2^8 + 14(1^8) |
| 271 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 15(1^6) | 2(2^7) + 15(1^7) | 2^8 + 15(1^8) |
| 272 | ^2 + ^2 | ^3 + ^3 | 4^4 + 2^4 | ^5 + ^5 | 4(2^6) + 16(1^6) | 2(2^7) + 16(1^7) | 2^8 + 16(1^8) |
| 273 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 17(1^6) | 2(2^7) + 17(1^7) | 2^8 + 17(1^8) |
| 274 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 18(1^6) | 2(2^7) + 18(1^7) | 2^8 + 18(1^8) |
| 275 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 2^5 | 4(2^6) + 19(1^6) | 2(2^7) + 19(1^7) | 2^8 + 19(1^8) |
| 276 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 2^5 + 1^5 | 4(2^6) + 20(1^6) | 2(2^7) + 20(1^7) | 2^8 + 20(1^8) |
| 277 | 14^2 + 9^2 | 2(5^3) + 3^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 21(1^6) | 2(2^7) + 21(1^7) | 2^8 + 21(1^8) |
| 278 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 22(1^6) | 2(2^7) + 22(1^7) | 2^8 + 22(1^8) |
| 279 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 23(1^6) | 2(2^7) + 23(1^7) | 2^8 + 23(1^8) |
| 280 | ^2 + ^2 | 6^3 + 4^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 24(1^6) | 2(2^7) + 24(1^7) | 2^8 + 24(1^8) |
| 281 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 25(1^6) | 2(2^7) + 25(1^7) | 2^8 + 25(1^8) |
| 282 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 26(1^6) | 2(2^7) + 26(1^7) | 2^8 + 26(1^8) |
| 283 | ^2 + ^2 | 4(4^3) + 3^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 27(1^6) | 2(2^7) + 27(1^7) | 2^8 + 27(1^8) |
| 284 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 28(1^6) | 2(2^7) + 28(1^7) | 2^8 + 28(1^8) |
| 285 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 29(1^6) | 2(2^7) + 29(1^7) | 2^8 + 29(1^8) |
| 286 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 30(1^6) | 2(2^7) + 30(1^7) | 2^8 + 30(1^8) |
| 287 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 31(1^6) | 2(2^7) + 31(1^7) | 2^8 + 31(1^8) |
| 288 | 2(12^2) | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 32(1^6) | 2(2^7) + 32(1^7) | 2^8 + 32(1^8) |
| 289 | 17^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 33(1^6) | 2(2^7) + 33(1^7) | 2^8 + 33(1^8) |
| 290 | 13^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 34(1^6) | 2(2^7) + 34(1^7) | 2^8 + 34(1^8) |
| 291 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 35(1^6) | 2(2^7) + 35(1^7) | 2^8 + 35(1^8) |
| 292 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 36(1^6) | 2(2^7) + 36(1^7) | 2^8 + 36(1^8) |
| 293 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 37(1^6) | 2(2^7) + 37(1^7) | 2^8 + 37(1^8) |
| 294 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 38(1^6) | 2(2^7) + 38(1^7) | 2^8 + 38(1^8) |
| 295 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 39(1^6) | 2(2^7) + 39(1^7) | 2^8 + 39(1^8) |
| 296 | 14^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 40(1^6) | 2(2^7) + 40(1^7) | 2^8 + 40(1^8) |
| 297 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 41(1^6) | 2(2^7) + 41(1^7) | 2^8 + 41(1^8) |
| 298 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 42(1^6) | 2(2^7) + 42(1^7) | 2^8 + 42(1^8) |
| 299 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 43(1^6) | 2(2^7) + 43(1^7) | 2^8 + 43(1^8) |
| 300 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 44(1^6) | 2(2^7) + 44(1^7) | 2^8 + 44(1^8) |
| 301 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 45(1^6) | 2(2^7) + 45(1^7) | 2^8 + 45(1^8) |
| 302 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 46(1^6) | 2(2^7) + 46(1^7) | 2^8 + 46(1^8) |
| 303 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 47(1^6) | 2(2^7) + 47(1^7) | 2^8 + 47(1^8) |
| 304 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 48(1^6) | 2(2^7) + 48(1^7) | 2^8 + 48(1^8) |
| 305 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 49(1^6) | 2(2^7) + 49(1^7) | 2^8 + 49(1^8) |
| 306 | 15^2 + 9^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 50(1^6) | 2(2^7) + 50(1^7) | 2^8 + 50(1^8) |
| 307 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 2(2^5) | 4(2^6) + 51(1^6) | 2(2^7) + 51(1^7) | 2^8 + 51(1^8) |
| 308 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 52(1^6) | 2(2^7) + 52(1^7) | 2^8 + 52(1^8) |
| 309 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 53(1^6) | 2(2^7) + 53(1^7) | 2^8 + 53(1^8) |
| 310 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 54(1^6) | 2(2^7) + 54(1^7) | 2^8 + 54(1^8) |
| 311 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 55(1^6) | 2(2^7) + 55(1^7) | 2^8 + 55(1^8) |
| 312 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 56(1^6) | 2(2^7) + 56(1^7) | 2^8 + 56(1^8) |
| 313 | 13^2 + 12^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 57(1^6) | 2(2^7) + 57(1^7) | 2^8 + 57(1^8) |
| 314 | ^2 + ^2 | 2(5^3) + 4^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 58(1^6) | 2(2^7) + 58(1^7) | 2^8 + 58(1^8) |
| 315 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 59(1^6) | 2(2^7) + 59(1^7) | 2^8 + 59(1^8) |
| 316 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 60(1^6) | 2(2^7) + 60(1^7) | 2^8 + 60(1^8) |
| 317 | 14^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 61(1^6) | 2(2^7) + 61(1^7) | 2^8 + 61(1^8) |
| 318 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 62(1^6) | 2(2^7) + 62(1^7) | 2^8 + 62(1^8) |
| 319 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 4(2^6) + 63(1^6) | 2(2^7) + 63(1^7) | 2^8 + 63(1^8) |
| 320 | 16^2 + 8^2 | 5(4^3) | ^4 + ^4 | ^5 + ^5 | 5(2^6) | 2(2^7) + 64(1^7) | 2^8 + 64(1^8) |
| 321 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 1^6 | 2(2^7) + 65(1^7) | 2^8 + 65(1^8) |
| 322 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 2(1^6) | 2(2^7) + 66(1^7) | 2^8 + 66(1^8) |
| 323 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 3(1^6) | 2(2^7) + 67(1^7) | 2^8 + 67(1^8) |
| 324 | 18^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 4(1^6) | 2(2^7) + 68(1^7) | 2^8 + 68(1^8) |
| 325 | 15^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 5(1^6) | 2(2^7) + 69(1^7) | 2^8 + 69(1^8) |
| 326 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 6(1^6) | 2(2^7) + 70(1^7) | 2^8 + 70(1^8) |
| 327 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 7(1^6) | 2(2^7) + 71(1^7) | 2^8 + 71(1^8) |
| 328 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 8(1^6) | 2(2^7) + 72(1^7) | 2^8 + 72(1^8) |
| 329 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 9(1^6) | 2(2^7) + 73(1^7) | 2^8 + 73(1^8) |
| 330 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 10(1^6) | 2(2^7) + 74(1^7) | 2^8 + 74(1^8) |
| 331 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 11(1^6) | 2(2^7) + 75(1^7) | 2^8 + 75(1^8) |
| 332 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 12(1^6) | 2(2^7) + 76(1^7) | 2^8 + 76(1^8) |
| 333 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 13(1^6) | 2(2^7) + 77(1^7) | 2^8 + 77(1^8) |
| 334 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 14(1^6) | 2(2^7) + 78(1^7) | 2^8 + 78(1^8) |
| 335 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 15(1^6) | 2(2^7) + 79(1^7) | 2^8 + 79(1^8) |
| 336 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 16(1^6) | 2(2^7) + 80(1^7) | 2^8 + 80(1^8) |
| 337 | 16^2 + 9^2 | ^3 + ^3 | 4^4 + 3^4 | ^5 + ^5 | 5(2^6) + 17(1^6) | 2(2^7) + 81(1^7) | 2^8 + 81(1^8) |
| 338 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 18(1^6) | 2(2^7) + 82(1^7) | 2^8 + 82(1^8) |
| 339 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 3(2^5) | 5(2^6) + 19(1^6) | 2(2^7) + 83(1^7) | 2^8 + 83(1^8) |
| 340 | 14^2 + 12^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 20(1^6) | 2(2^7) + 84(1^7) | 2^8 + 84(1^8) |
| 341 | ^2 + ^2 | 6^3 + 5^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 21(1^6) | 2(2^7) + 85(1^7) | 2^8 + 85(1^8) |
| 342 | ^2 + ^2 | 6^3 + 5^3 + 1^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 22(1^6) | 2(2^7) + 86(1^7) | 2^8 + 86(1^8) |
| 343 | ^2 + ^2 | 7^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 23(1^6) | 2(2^7) + 87(1^7) | 2^8 + 87(1^8) |
| 344 | ^2 + ^2 | 7^3 + 1^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 24(1^6) | 2(2^7) + 88(1^7) | 2^8 + 88(1^8) |
| 345 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 25(1^6) | 2(2^7) + 89(1^7) | 2^8 + 89(1^8) |
| 346 | 15^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 26(1^6) | 2(2^7) + 90(1^7) | 2^8 + 90(1^8) |
| 347 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 27(1^6) | 2(2^7) + 91(1^7) | 2^8 + 91(1^8) |
| 348 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 28(1^6) | 2(2^7) + 92(1^7) | 2^8 + 92(1^8) |
| 349 | ^2 + ^2 | 6^3 + 5^3 + 2^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 29(1^6) | 2(2^7) + 93(1^7) | 2^8 + 93(1^8) |
| 350 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 30(1^6) | 2(2^7) + 94(1^7) | 2^8 + 94(1^8) |
| 351 | ^2 + ^2 | 7^3 + 2^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 31(1^6) | 2(2^7) + 95(1^7) | 2^8 + 95(1^8) |
| 352 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 32(1^6) | 2(2^7) + 96(1^7) | 2^8 + 96(1^8) |
| 353 | 17^2 + 8^2 | ^3 + ^3 | 4^4 + 3^4 + 2^4 | ^5 + ^5 | 5(2^6) + 33(1^6) | 2(2^7) + 97(1^7) | 2^8 + 97(1^8) |
| 354 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 34(1^6) | 2(2^7) + 98(1^7) | 2^8 + 98(1^8) |
| 355 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 35(1^6) | 2(2^7) + 99(1^7) | 2^8 + 99(1^8) |
| 356 | 16^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 36(1^6) | 2(2^7) + 100(1^7) | 2^8 + 100(1^8) |
| 357 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 37(1^6) | 2(2^7) + 101(1^7) | 2^8 + 101(1^8) |
| 358 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 38(1^6) | 2(2^7) + 102(1^7) | 2^8 + 102(1^8) |
| 359 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 39(1^6) | 2(2^7) + 103(1^7) | 2^8 + 103(1^8) |
| 360 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 40(1^6) | 2(2^7) + 104(1^7) | 2^8 + 104(1^8) |
| 361 | 19^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 41(1^6) | 2(2^7) + 105(1^7) | 2^8 + 105(1^8) |
| 362 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 42(1^6) | 2(2^7) + 106(1^7) | 2^8 + 106(1^8) |
| 363 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 43(1^6) | 2(2^7) + 107(1^7) | 2^8 + 107(1^8) |
| 364 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 44(1^6) | 2(2^7) + 108(1^7) | 2^8 + 108(1^8) |
| 365 | 14^2 + 13^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 45(1^6) | 2(2^7) + 109(1^7) | 2^8 + 109(1^8) |
| 366 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 46(1^6) | 2(2^7) + 110(1^7) | 2^8 + 110(1^8) |
| 367 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 47(1^6) | 2(2^7) + 111(1^7) | 2^8 + 111(1^8) |
| 368 | ^2 + ^2 | 6^3 + 5^3 + 3^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 48(1^6) | 2(2^7) + 112(1^7) | 2^8 + 112(1^8) |
| 369 | 15^2 + 12^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 49(1^6) | 2(2^7) + 113(1^7) | 2^8 + 113(1^8) |
| 370 | 17^2 + 9^2 | 3^3 + 7^3 + 0^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 50(1^6) | 2(2^7) + 114(1^7) | 2^8 + 114(1^8) |
| 371 | ^2 + ^2 | 3^3 + 7^3 + 1^3 | ^4 + ^4 | 3^5 + 4(2^5) | 5(2^6) + 51(1^6) | 2(2^7) + 115(1^7) | 2^8 + 115(1^8) |
| 372 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 52(1^6) | 2(2^7) + 116(1^7) | 2^8 + 116(1^8) |
| 373 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 53(1^6) | 2(2^7) + 117(1^7) | 2^8 + 117(1^8) |
| 374 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 54(1^6) | 2(2^7) + 118(1^7) | 2^8 + 118(1^8) |
| 375 | ^2 + ^2 | 3(5^3) | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 55(1^6) | 2(2^7) + 119(1^7) | 2^8 + 119(1^8) |
| 376 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 56(1^6) | 2(2^7) + 120(1^7) | 2^8 + 120(1^8) |
| 377 | 16^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 57(1^6) | 2(2^7) + 121(1^7) | 2^8 + 121(1^8) |
| 378 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 58(1^6) | 2(2^7) + 122(1^7) | 2^8 + 122(1^8) |
| 379 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 59(1^6) | 2(2^7) + 123(1^7) | 2^8 + 123(1^8) |
| 380 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 60(1^6) | 2(2^7) + 124(1^7) | 2^8 + 124(1^8) |
| 381 | ^2 + ^2 | 5^3 + 4(4^3) | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 61(1^6) | 2(2^7) + 125(1^7) | 2^8 + 125(1^8) |
| 382 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 62(1^6) | 2(2^7) + 126(1^7) | 2^8 + 126(1^8) |
| 383 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 5(2^6) + 63(1^6) | 2(2^7) + 127(1^7) | 2^8 + 127(1^8) |
| 384 | ^2 + ^2 | 6(4^3) | ^4 + ^4 | ^5 + ^5 | 6(2^6) | 3(2^7) | 2^8 + 128(1^8) |
| 385 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 1^6 | 3(2^7) + 1^7 | 2^8 + 129(1^8) |
| 386 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 2(1^6) | 3(2^7) + 2(1^7) | 2^8 + 130(1^8) |
| 387 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 3(1^6) | 3(2^7) + 3(1^7) | 2^8 + 131(1^8) |
| 388 | 18^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 4(1^6) | 3(2^7) + 4(1^7) | 2^8 + 132(1^8) |
| 389 | 17^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 5(1^6) | 3(2^7) + 5(1^7) | 2^8 + 133(1^8) |
| 390 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 6(1^6) | 3(2^7) + 6(1^7) | 2^8 + 134(1^8) |
| 391 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 7(1^6) | 3(2^7) + 7(1^7) | 2^8 + 135(1^8) |
| 392 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 8(1^6) | 3(2^7) + 8(1^7) | 2^8 + 136(1^8) |
| 393 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 9(1^6) | 3(2^7) + 9(1^7) | 2^8 + 137(1^8) |
| 394 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 10(1^6) | 3(2^7) + 10(1^7) | 2^8 + 138(1^8) |
| 395 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 11(1^6) | 3(2^7) + 11(1^7) | 2^8 + 139(1^8) |
| 396 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 12(1^6) | 3(2^7) + 12(1^7) | 2^8 + 140(1^8) |
| 397 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 13(1^6) | 3(2^7) + 13(1^7) | 2^8 + 141(1^8) |
| 398 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 14(1^6) | 3(2^7) + 14(1^7) | 2^8 + 142(1^8) |
| 399 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 15(1^6) | 3(2^7) + 15(1^7) | 2^8 + 143(1^8) |
| 400 | 20^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 16(1^6) | 3(2^7) + 16(1^7) | 2^8 + 144(1^8) |
| 401 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 17(1^6) | 3(2^7) + 17(1^7) | 2^8 + 145(1^8) |
| 402 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 18(1^6) | 3(2^7) + 18(1^7) | 2^8 + 146(1^8) |
| 403 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 5(2^5) | 6(2^6) + 19(1^6) | 3(2^7) + 19(1^7) | 2^8 + 147(1^8) |
| 404 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 20(1^6) | 3(2^7) + 20(1^7) | 2^8 + 148(1^8) |
| 405 | 18^2 + 9^2 | 6^3 + 5^3 + 4^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 21(1^6) | 3(2^7) + 21(1^7) | 2^8 + 149(1^8) |
| 406 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 22(1^6) | 3(2^7) + 22(1^7) | 2^8 + 150(1^8) |
| 407 | ^2 + ^2 | 4^3 + 0^3 + 7^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 23(1^6) | 3(2^7) + 23(1^7) | 2^8 + 151(1^8) |
| 408 | ^2 + ^2 | 7^3 + 4^3 + 1^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 24(1^6) | 3(2^7) + 24(1^7) | 2^8 + 152(1^8) |
| 409 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 25(1^6) | 3(2^7) + 25(1^7) | 2^8 + 153(1^8) |
| 410 | 17^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 26(1^6) | 3(2^7) + 26(1^7) | 2^8 + 154(1^8) |
| 411 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 27(1^6) | 3(2^7) + 27(1^7) | 2^8 + 155(1^8) |
| 412 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 28(1^6) | 3(2^7) + 28(1^7) | 2^8 + 156(1^8) |
| 413 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 29(1^6) | 3(2^7) + 29(1^7) | 2^8 + 157(1^8) |
| 414 | ^2 + ^2 | ^3 + ^3 | 4^4 + 2(3^4) | ^5 + ^5 | 6(2^6) + 30(1^6) | 3(2^7) + 30(1^7) | 2^8 + 158(1^8) |
| 415 | ^2 + ^2 | 7^3 + 4^3 + 2^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 31(1^6) | 3(2^7) + 31(1^7) | 2^8 + 159(1^8) |
| 416 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 32(1^6) | 3(2^7) + 32(1^7) | 2^8 + 160(1^8) |
| 417 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 33(1^6) | 3(2^7) + 33(1^7) | 2^8 + 161(1^8) |
| 418 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 34(1^6) | 3(2^7) + 34(1^7) | 2^8 + 162(1^8) |
| 419 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 35(1^6) | 3(2^7) + 35(1^7) | 2^8 + 163(1^8) |
| 420 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 36(1^6) | 3(2^7) + 36(1^7) | 2^8 + 164(1^8) |
| 421 | 15^2 + 14^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 37(1^6) | 3(2^7) + 37(1^7) | 2^8 + 165(1^8) |
| 422 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 38(1^6) | 3(2^7) + 38(1^7) | 2^8 + 166(1^8) |
| 423 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 39(1^6) | 3(2^7) + 39(1^7) | 2^8 + 167(1^8) |
| 424 | 18^2 + 10^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 40(1^6) | 3(2^7) + 40(1^7) | 2^8 + 168(1^8) |
| 425 | 19^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 41(1^6) | 3(2^7) + 41(1^7) | 2^8 + 169(1^8) |
| 426 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 42(1^6) | 3(2^7) + 42(1^7) | 2^8 + 170(1^8) |
| 427 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 43(1^6) | 3(2^7) + 43(1^7) | 2^8 + 171(1^8) |
| 428 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 44(1^6) | 3(2^7) + 44(1^7) | 2^8 + 172(1^8) |
| 429 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 45(1^6) | 3(2^7) + 45(1^7) | 2^8 + 173(1^8) |
| 430 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 46(1^6) | 3(2^7) + 46(1^7) | 2^8 + 174(1^8) |
| 431 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 47(1^6) | 3(2^7) + 47(1^7) | 2^8 + 175(1^8) |
| 432 | ^2 + ^2 | 2(6^3) | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 48(1^6) | 3(2^7) + 48(1^7) | 2^8 + 176(1^8) |
| 433 | 17^2 + 12^2 | 2(6^3) + 1^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 49(1^6) | 3(2^7) + 49(1^7) | 2^8 + 177(1^8) |
| 434 | ^2 + ^2 | 7^3 + 4^3 + 3^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 50(1^6) | 3(2^7) + 50(1^7) | 2^8 + 178(1^8) |
| 435 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 3^5 + 6(2^5) | 6(2^6) + 51(1^6) | 3(2^7) + 51(1^7) | 2^8 + 179(1^8) |
| 436 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 52(1^6) | 3(2^7) + 52(1^7) | 2^8 + 180(1^8) |
| 437 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 53(1^6) | 3(2^7) + 53(1^7) | 2^8 + 181(1^8) |
| 438 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 54(1^6) | 3(2^7) + 54(1^7) | 2^8 + 182(1^8) |
| 439 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 55(1^6) | 3(2^7) + 55(1^7) | 2^8 + 183(1^8) |
| 440 | ^2 + ^2 | 2(6^3) + 2^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 56(1^6) | 3(2^7) + 56(1^7) | 2^8 + 184(1^8) |
| 441 | 21^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 57(1^6) | 3(2^7) + 57(1^7) | 2^8 + 185(1^8) |
| 442 | 19^2 + 9^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 58(1^6) | 3(2^7) + 58(1^7) | 2^8 + 186(1^8) |
| 443 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 59(1^6) | 3(2^7) + 59(1^7) | 2^8 + 187(1^8) |
| 444 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 60(1^6) | 3(2^7) + 60(1^7) | 2^8 + 188(1^8) |
| 445 | 18^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 61(1^6) | 3(2^7) + 61(1^7) | 2^8 + 189(1^8) |
| 446 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 62(1^6) | 3(2^7) + 62(1^7) | 2^8 + 190(1^8) |
| 447 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 6(2^6) + 63(1^6) | 3(2^7) + 63(1^7) | 2^8 + 191(1^8) |
| 448 | ^2 + ^2 | 7(4^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) | 3(2^7) + 64(1^7) | 2^8 + 192(1^8) |
| 449 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 1^6 | 3(2^7) + 65(1^7) | 2^8 + 193(1^8) |
| 450 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 2(1^6) | 3(2^7) + 66(1^7) | 2^8 + 194(1^8) |
| 451 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 3(1^6) | 3(2^7) + 67(1^7) | 2^8 + 195(1^8) |
| 452 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 4(1^6) | 3(2^7) + 68(1^7) | 2^8 + 196(1^8) |
| 453 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 5(1^6) | 3(2^7) + 69(1^7) | 2^8 + 197(1^8) |
| 454 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 6(1^6) | 3(2^7) + 70(1^7) | 2^8 + 198(1^8) |
| 455 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 7(1^6) | 3(2^7) + 71(1^7) | 2^8 + 199(1^8) |
| 456 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 8(1^6) | 3(2^7) + 72(1^7) | 2^8 + 200(1^8) |
| 457 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 9(1^6) | 3(2^7) + 73(1^7) | 2^8 + 201(1^8) |
| 458 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 10(1^6) | 3(2^7) + 74(1^7) | 2^8 + 202(1^8) |
| 459 | ^2 + ^2 | 2(6^3) + 3^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 11(1^6) | 3(2^7) + 75(1^7) | 2^8 + 203(1^8) |
| 460 | ^2 + ^2 | 2(6^3) + 3^3 + 1^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 12(1^6) | 3(2^7) + 76(1^7) | 2^8 + 204(1^8) |
| 461 | 19^2 + 10^2 | 2(6^3) + 3^3 + 2(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 13(1^6) | 3(2^7) + 77(1^7) | 2^8 + 205(1^8) |
| 462 | ^2 + ^2 | 2(6^3) + 3^3 + 3(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 14(1^6) | 3(2^7) + 78(1^7) | 2^8 + 206(1^8) |
| 463 | ^2 + ^2 | 2(6^3) + 3^3 + 4(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 15(1^6) | 3(2^7) + 79(1^7) | 2^8 + 207(1^8) |
| 464 | 20^2 + 8^2 | 2(6^3) + 3^3 + 5(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 16(1^6) | 3(2^7) + 80(1^7) | 2^8 + 208(1^8) |
| 465 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 17(1^6) | 3(2^7) + 81(1^7) | 2^8 + 209(1^8) |
| 466 | ^2 + ^2 | 6^3 + 2(5^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 18(1^6) | 3(2^7) + 82(1^7) | 2^8 + 210(1^8) |
| 467 | ^2 + ^2 | 6^3 + 2(5^3) + 1^3 | ^4 + ^4 | 3^5 + 7(2^5) | 7(2^6) + 19(1^6) | 3(2^7) + 83(1^7) | 2^8 + 211(1^8) |
| 468 | 18^2 + 12^2 | 7^3 + 5^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 20(1^6) | 3(2^7) + 84(1^7) | 2^8 + 212(1^8) |
| 469 | ^2 + ^2 | 7^3 + 5^3 + 1^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 21(1^6) | 3(2^7) + 85(1^7) | 2^8 + 213(1^8) |
| 470 | ^2 + ^2 | 7^3 + 5^3 + 2(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 22(1^6) | 3(2^7) + 86(1^7) | 2^8 + 214(1^8) |
| 471 | ^2 + ^2 | 7^3 + 2(4^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 23(1^6) | 3(2^7) + 87(1^7) | 2^8 + 215(1^8) |
| 472 | ^2 + ^2 | 6^3 + 4(4^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 24(1^6) | 3(2^7) + 88(1^7) | 2^8 + 216(1^8) |
| 473 | ^2 + ^2 | 7^3 + 2(4^3) + 2(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 25(1^6) | 3(2^7) + 89(1^7) | 2^8 + 217(1^8) |
| 474 | ^2 + ^2 | 7^3 + 2(4^3) + 3(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 26(1^6) | 3(2^7) + 90(1^7) | 2^8 + 218(1^8) |
| 475 | ^2 + ^2 | 7^3 + 2(4^3) + 4(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 27(1^6) | 3(2^7) + 91(1^7) | 2^8 + 219(1^8) |
| 476 | ^2 + ^2 | 7^3 + 5^3 + 2^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 28(1^6) | 3(2^7) + 92(1^7) | 2^8 + 220(1^8) |
| 477 | ^2 + ^2 | 7^3 + 5^3 + 2^3 + 1^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 29(1^6) | 3(2^7) + 93(1^7) | 2^8 + 221(1^8) |
| 478 | ^2 + ^2 | 7^3 + 5^3 + 2^3 + 2(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 30(1^6) | 3(2^7) + 94(1^7) | 2^8 + 222(1^8) |
| 479 | ^2 + ^2 | 7^3 + 5^3 + 2^3 + 3(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 31(1^6) | 3(2^7) + 95(1^7) | 2^8 + 223(1^8) |
| 480 | ^2 + ^2 | 7^3 + 5^3 + 2^3 + 4(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 32(1^6) | 3(2^7) + 96(1^7) | 2^8 + 224(1^8) |
| 481 | 16^2 + 15^2 | 7^3 + 5^3 + 2^3 + 5(1^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 33(1^6) | 3(2^7) + 97(1^7) | 2^8 + 225(1^8) |
| 482 | 19^2 + 11^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 34(1^6) | 3(2^7) + 98(1^7) | 2^8 + 226(1^8) |
| 483 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 35(1^6) | 3(2^7) + 99(1^7) | 2^8 + 227(1^8) |
| 484 | 22^2 | 7^3 + 5^3 + 2(2^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 36(1^6) | 3(2^7) + 100(1^7) | 2^8 + 228(1^8) |
| 485 | ^2 + ^2 | 7^3 + 5^3 + 2(2^3) + 1^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 37(1^6) | 3(2^7) + 101(1^7) | 2^8 + 229(1^8) |
| 486 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | 2(3^5) | 7(2^6) + 38(1^6) | 3(2^7) + 102(1^7) | 2^8 + 230(1^8) |
| 487 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 39(1^6) | 3(2^7) + 103(1^7) | 2^8 + 231(1^8) |
| 488 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 40(1^6) | 3(2^7) + 104(1^7) | 2^8 + 232(1^8) |
| 489 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 41(1^6) | 3(2^7) + 105(1^7) | 2^8 + 233(1^8) |
| 490 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 42(1^6) | 3(2^7) + 106(1^7) | 2^8 + 234(1^8) |
| 491 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 43(1^6) | 3(2^7) + 107(1^7) | 2^8 + 235(1^8) |
| 492 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 44(1^6) | 3(2^7) + 108(1^7) | 2^8 + 236(1^8) |
| 493 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 45(1^6) | 3(2^7) + 109(1^7) | 2^8 + 237(1^8) |
| 494 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 46(1^6) | 3(2^7) + 110(1^7) | 2^8 + 238(1^8) |
| 495 | ^2 + ^2 | 7^3 + 5^3 + 3^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 47(1^6) | 3(2^7) + 111(1^7) | 2^8 + 239(1^8) |
| 496 | ^2 + ^2 | 2(6^3) + 4^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 48(1^6) | 3(2^7) + 112(1^7) | 2^8 + 240(1^8) |
| 497 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 49(1^6) | 3(2^7) + 113(1^7) | 2^8 + 241(1^8) |
| 498 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 50(1^6) | 3(2^7) + 114(1^7) | 2^8 + 242(1^8) |
| 499 | ^2 + ^2 | ^3 + ^3 | 4^4 + 3(3^4) | 3^5 + 8(2^5) | 7(2^6) + 51(1^6) | 3(2^7) + 115(1^7) | 2^8 + 243(1^8) |
| 500 | 20^2 + 10^2 | 4(5^3) | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 52(1^6) | 3(2^7) + 116(1^7) | 2^8 + 244(1^8) |
| 501 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 53(1^6) | 3(2^7) + 117(1^7) | 2^8 + 245(1^8) |
| 502 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 54(1^6) | 3(2^7) + 118(1^7) | 2^8 + 246(1^8) |
| 503 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 55(1^6) | 3(2^7) + 119(1^7) | 2^8 + 247(1^8) |
| 504 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 56(1^6) | 3(2^7) + 120(1^7) | 2^8 + 248(1^8) |
| 505 | 21^2 + 8^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 57(1^6) | 3(2^7) + 121(1^7) | 2^8 + 249(1^8) |
| 506 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 58(1^6) | 3(2^7) + 122(1^7) | 2^8 + 250(1^8) |
| 507 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 59(1^6) | 3(2^7) + 123(1^7) | 2^8 + 251(1^8) |
| 508 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 60(1^6) | 3(2^7) + 124(1^7) | 2^8 + 252(1^8) |
| 509 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 61(1^6) | 3(2^7) + 125(1^7) | 2^8 + 253(1^8) |
| 510 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 62(1^6) | 3(2^7) + 126(1^7) | 2^8 + 254(1^8) |
| 511 | ^2 + ^2 | ^3 + ^3 | ^4 + ^4 | ^5 + ^5 | 7(2^6) + 63(1^6) | 3(2^7) + 127(1^7) | 2^8 + 255(1^8) |
| 512 | 2(16^2) | 8^3 | 2(4^4) | 16(2^5) | 8(2^6) | 4(2^7) | 2(2^8) |
| 2^9 |
| Friedman representations that are also efficient Waring representations. | Narcissistic representations that are also efficient Waring representations (though (0^k)s are technically not allowed in Waring representations. Also, for these we deviate from sorting the powers from largest base to smallest base). |
Several sequences from Sloane's Online Encyclopedia of Integer Sequences were very helpful in the compilation of this table. First of all, Sloane's A002804, which tells us what is the maximum number of kth powers needed to sum up to any integer (as of this writing, the sequence is presented as a "presumed" solution to Waring's problem, but I can safely say that these maximums are correct in the small range I've explored).
Then there's Sloane's A004215, which tells us which integers can not be expressed as a sum of fewer than four squares. Every time I came up with a four-square solution for an integer, I checked if that integer was listed in A004215. If it wasn't, that told me "You can do better," and it took a little more searching, but I was able to get such cases down to three squares.
In general, every time I came up with a solution using the maximum number of kth powers, I checked to see if I could find a solution using at least one fewer power. Of course, it's possible that when I came up with solutions that are one less than the maximum, there are much better solutions of even fewer powers. This is most likely with cubes.
Also helpful, Sloane's A007692, which tells us which integers can be expressed as a sum of two squares in two different ways. In the table, only one solution of squaresums is given for each integer, but A007692 helped me make decisions as to which form is more elegant, and therefore which one to include in the table. (However, depending on your browser, if you put your mouse over some cells, a tooltip will come up with the other squaresum expression).
Of course when two solutions use the same number of kth powers it is difficult to say which one is more elegant. In general, I prefer solutions of distinct powers, none of which is 1^k. Perhaps I feel more strongly about not liking 1^k than I feel about not liking repeated bases, which is why I chose 50 = 2(5^2) over 50 = 7^2 + 1^2.
If you come up with a solution for a given integer that you think is more elegant than the one given in the table, even if it's the same number of powers, please e-mail me. If I use it in the table, I will give you credit on this page.
As noted above, the table does not list solutions of the form n(1^k), though for n between 2^k and 3^k the solutions are almost as boring, specifically, 2^k + (n - 2^k)(1^k). It is after 3^k that the solutions get more interesting, but also trickier to find.