A034681 Sum of seventh powers of unitary divisors.

1, 129, 2188, 16385, 78126, 282252, 823544, 2097153, 4782970, 10078254, 19487172, 35850380, 62748518, 106237176, 170939688, 268435457, 410338674, 617003130, 893871740, 1280094510, 1801914272, 2513845188, 3404825448

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: A351270 A088719 A321563 * A351302 A017677 A013955

Adjacent sequences: A034678 A034679 A034680 * A034682 A034683 A034684

Keyword

nonn,mult

Author

Erich Friedman

Status

approved