A034681 - OEIS

%I #17 Aug 10 2019 04:53:30

%S 1,129,2188,16385,78126,282252,823544,2097153,4782970,10078254,

%T 19487172,35850380,62748518,106237176,170939688,268435457,410338674,

%U 617003130,893871740,1280094510,1801914272,2513845188,3404825448

%N Sum of seventh powers of unitary divisors.

%H Amiram Eldar, <a href="/A034681/b034681.txt">Table of n, a(n) for n = 1..10000</a>

%F Dirichlet g.f.: zeta(s)*zeta(s-7)/zeta(2s-7). - _R. J. Mathar_, Apr 12 2011

%F If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(7*k_j)). - _Ilya Gutkovskiy_, Nov 04 2018

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

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

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

%Y Cf. A034444, A034448.

%Y Row n=7 of A286880.

%K nonn,mult

%O 1,2

%A _Erich Friedman_