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

Author

Erich Friedman

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A034444, A034448.

Row n=7 of A286880.

Programs

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 *)

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