%I #17 Aug 10 2019 04:53:01
%S 1,33,244,1025,3126,8052,16808,32769,59050,103158,161052,250100,
%T 371294,554664,762744,1048577,1419858,1948650,2476100,3204150,4101152,
%U 5314716,6436344,7995636,9765626,12252702,14348908,17228200,20511150,25170552
%N Sum of fifth powers of unitary divisors.
%H Amiram Eldar, <a href="/A034679/b034679.txt">Table of n, a(n) for n = 1..10000</a>
%F Dirichlet g.f.: zeta(s)*zeta(s-5)/zeta(2s-5). - _R. J. Mathar_, Apr 12 2011
%F If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(5*k_j)). - _Ilya Gutkovskiy_, Nov 04 2018
%F Sum_{k=1..n} a(k) ~ (Pi*n)^6 / (5670*Zeta(7)). - _Vaclav Kotesovec_, Feb 07 2019
%t Table[Total[Select[Divisors[n], CoprimeQ[#, n/#] &]^5], {n, 1, 50}] (* _Vaclav Kotesovec_, Feb 07 2019 *)
%t a[1] = 1; a[n_] := Times @@ (1 + First[#]^(5*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* _Amiram Eldar_, Aug 10 2019 *)
%Y Cf. A034444, A034448.
%Y Row n=5 of A286880.
%K nonn,mult
%O 1,2
%A _Erich Friedman_
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