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%I #19 Aug 10 2019 04:52:27
%S 1,257,6562,65537,390626,1686434,5764802,16777217,43046722,100390882,
%T 214358882,430053794,815730722,1481554114,2563287812,4294967297,
%U 6975757442,11063007554,16983563042,25600456162,37828630724
%N Sum of eighth powers of unitary divisors.
%H Amiram Eldar, <a href="/A034682/b034682.txt">Table of n, a(n) for n = 1..10000</a>
%F Dirichlet g.f.: zeta(s)*zeta(s-8)/zeta(2s-8). - _R. J. Mathar_, Apr 12 2011
%F If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(8*k_j)). - _Ilya Gutkovskiy_, Nov 04 2018
%F Sum_{k=1..n} a(k) ~ 10395*Zeta(9)*n^9 / Pi^10. - _Vaclav Kotesovec_, Feb 07 2019
%t Table[Total[Select[Divisors[n], CoprimeQ[#, n/#] &]^8], {n, 1, 50}] (* _Vaclav Kotesovec_, Feb 07 2019 *)
%t a[1] = 1; a[n_] := Times @@ (1 + First[#]^(8*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* _Amiram Eldar_, Aug 10 2019 *)
%Y Cf. A034444, A034448.
%Y Row n=8 of A286880.
%K nonn,mult
%O 1,2
%A _Erich Friedman_
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