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A034681 Sum of seventh powers of unitary divisors. 2
1, 129, 2188, 16385, 78126, 282252, 823544, 2097153, 4782970, 10078254, 19487172, 35850380, 62748518, 106237176, 170939688, 268435457, 410338674, 617003130, 893871740, 1280094510, 1801914272, 2513845188, 3404825448 (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-7)/zeta(2s-7). - R. J. Mathar, Apr 12 2011

If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(7*k_j)). - Ilya Gutkovskiy, Nov 04 2018

Sum_{k=1..n} a(k) ~ (Pi*n)^8 / (75600*Zeta(9)). - Vaclav Kotesovec, Feb 07 2019

MATHEMATICA

Table[Total[Select[Divisors[n], CoprimeQ[#, n/#] &]^7], {n, 1, 50}] (* Vaclav Kotesovec, Feb 07 2019 *)

a[1] = 1; a[n_] := Times @@ (1 + First[#]^(7*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* Amiram Eldar, Aug 10 2019 *)

CROSSREFS

Cf. A034444, A034448.

Row n=7 of A286880.

Sequence in context: A240417 A088719 A321563 * A017677 A013955 A294302

Adjacent sequences:  A034678 A034679 A034680 * A034682 A034683 A034684

KEYWORD

nonn,mult

AUTHOR

Erich Friedman

STATUS

approved

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Last modified October 16 21:10 EDT 2019. Contains 328103 sequences. (Running on oeis4.)