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