A365019 Triangular numbers that for some k >= 0 are also the sum of the first k perfect powers.

0, 1, 159284476

Offset: 1

Author

Ilya Gutkovskiy, Aug 16 2023

Keywords

• nonn
• bref
• hard
• more

Examples

			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.
		

Crossrefs

Cf. A000217, A001597, A066527, A076408, A298270.

Programs

Mathematica

Join[{0}, Select[Accumulate[Select[Range[574564], # == 1 || GCD @@ FactorInteger[#][[All, 2]] > 1 &]], IntegerQ[Sqrt[8 # + 1]] &]]