A034679 Sum of fifth powers of unitary divisors.

1, 33, 244, 1025, 3126, 8052, 16808, 32769, 59050, 103158, 161052, 250100, 371294, 554664, 762744, 1048577, 1419858, 1948650, 2476100, 3204150, 4101152, 5314716, 6436344, 7995636, 9765626, 12252702, 14348908, 17228200, 20511150, 25170552

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

Dirichlet g.f.: zeta(s)*zeta(s-5)/zeta(2s-5). - R. J. Mathar, Apr 12 2011

If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(5*k_j)). - Ilya Gutkovskiy, Nov 04 2018

Sum_{k=1..n} a(k) ~ (Pi*n)^6 / (5670*Zeta(7)). - Vaclav Kotesovec, Feb 07 2019

Mathematica

Table[Total[Select[Divisors[n], CoprimeQ[#, n/#] &]^5], {n, 1, 50}] (* Vaclav Kotesovec, Feb 07 2019 *)
a[1] = 1; a[n_] := Times @@ (1 + First[#]^(5*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* Amiram Eldar, Aug 10 2019 *)

Crossrefs

Cf. A034444, A034448.

Row n=5 of A286880.

Sequence in context: A351268 A088703 A321561 * A351300 A017673 A001160

Adjacent sequences: A034676 A034677 A034678 * A034680 A034681 A034682

Keyword

nonn,mult

Author

Erich Friedman

Status

approved