A166605 Numbers k such that Sum_{i=1..k} i^5 divides Product_{i=1..k} i^5.

1, 13, 64, 95, 111, 118, 123, 133, 134, 140, 151, 177, 199, 217, 229, 242, 255, 264, 274, 281, 302, 305, 325, 333, 338, 354, 359, 365, 376, 394, 411, 414, 431, 433, 440, 472, 475, 477, 489, 514, 525, 528, 529, 537, 547, 569, 574, 583, 584, 585, 589, 594, 615

Offset: 1

Author

Alexander Adamchuk, Oct 18 2009

Keywords

• nonn

Examples

			a(2) = A125314(5) = 13.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A125314, A166602, A060462, A166604, A166606, A166607, A166608, A166609, A166610.

Programs

Mathematica

k = s = 1; p = 1; lst = {}; While[k < 100000, If[Mod[p, s] == 0, AppendTo[lst, k]]; k++; s = s + k^5; p = p*k^5]; lst  (* G. C. Greubel, May 18 2016 *)
Module[{nn=1000,i5},i5=Range[nn]^5;Position[Table[Times@@Take[i5,n]/Total[Take[i5,n]],{n,nn}],?IntegerQ]]//Flatten (* _Harvey P. Dale, Jan 18 2025 *)

Extensions

More terms from Max Alekseyev, Sep 29 2010