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.
%I A365019 #5 Aug 24 2023 10:33:51
%S A365019 0,1,159284476
%N A365019 Triangular numbers that for some k >= 0 are also the sum of the first k perfect powers.
%e A365019 159284476 is a term because 159284476 = 1 + 2 + 3 + 4 + ... + 17848 = 1 + 4 + 8 + 9 + ... + 574564 = 1^2 + 2^2 + 2^3 + 3^2 + ... + 758^2.
%t A365019 Join[{0}, Select[Accumulate[Select[Range[574564], # == 1 || GCD @@ FactorInteger[#][[All, 2]] > 1 &]], IntegerQ[Sqrt[8 # + 1]] &]]
%Y A365019 Cf. A000217, A001597, A066527, A076408, A298270.
%K A365019 nonn,bref,hard,more
%O A365019 1,3
%A A365019 _Ilya Gutkovskiy_, Aug 16 2023