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A034679 Sum of fifth powers of unitary divisors. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A178448 A088703 A321561 * A017673 A001160 A294300

Adjacent sequences:  A034676 A034677 A034678 * A034680 A034681 A034682

KEYWORD

nonn,mult

AUTHOR

Erich Friedman

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)