This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
a(2) = 129 = 1+64+64 = 4+4+121 = 16+49+64 = 4+25+100.
53 = 1^2 + 1^2 + 1^2 + 1^2 + 7^2
= 1^2 + 1^2 + 1^2 + 5^2 + 5^2
= 1^2 + 2^2 + 4^2 + 4^2 + 4^2
= 1^2 + 3^2 + 3^2 + 3^2 + 5^2
= 2^2 + 2^2 + 2^2 + 4^2 + 5^2.
1252 = 1^3 + 1^3 + 5^3 + 5^3 + 10^3
= 1^3 + 2^3 + 3^3 + 6^3 + 10^3
= 3^3 + 3^3 + 7^3 + 7^3 + 8^3
= 3^3 + 4^3 + 6^3 + 6^3 + 9^3.
20995 = 1^4 + 1^4 + 1^4 + 4^4 + 12^4
= 2^4 + 3^4 + 3^4 + 3^4 + 12^4
= 2^4 + 6^4 + 9^4 + 9^4 + 9^4
= 4^4 + 6^4 + 7^4 + 7^4 + 11^4.
287618651 = 8^5 + 21^5 + 27^5 + 27^5 + 48^5
= 9^5 + 13^5 + 26^5 + 37^5 + 46^5
= 11^5 + 12^5 + 23^5 + 41^5 + 44^5
= 11^5 + 20^5 + 22^5 + 30^5 + 48^5.
351060139210 = 8^6 + 50^6 + 53^6 + 56^6 + 81^6
= 18^6 + 43^6 + 49^6 + 64^6 + 80^6
= 27^6 + 31^6 + 56^6 + 62^6 + 80^6
= 35^6 + 36^6 + 38^6 + 73^6 + 76^6.
From _Ilya Gutkovskiy_, Aug 12 2024: (Start)
a(6) = 353563195 = 3^6 + 8^6 + 11^6 + 19^6 + 22^6 + 24^6
= 4^6 + 5^6 + 15^6 + 18^6 + 20^6 + 25^6
= 8^6 + 10^6 + 11^6 + 15^6 + 23^6 + 24^6
= 8^6 + 13^6 + 15^6 + 15^6 + 16^6 + 26^6. (End)
From _Ilya Gutkovskiy_, Aug 12 2024: (Start)
a(6) = 82718691 = 1^6 + 1^6 + 8^6 + 14^6 + 16^6 + 17^6 + 18^6
= 3^6 + 7^6 + 10^6 + 10^6 + 16^6 + 16^6 + 19^6
= 4^6 + 5^6 + 10^6 + 12^6 + 14^6 + 17^6 + 19^6
= 4^6 + 9^6 + 10^6 + 13^6 + 13^6 + 14^6 + 20^6. (End)