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%I
%S 1,65,730,4097,15626,47450,117650,262145,531442,1015690,1771562,
%T 2990810,4826810,7647250,11406980,16777217,24137570,34543730,47045882,
%U 64019722,85884500,115151530,148035890,191365850,244140626,313742650
%N Sum of sixth powers of unitary divisors.
%H Amiram Eldar, <a href="/A034680/b034680.txt">Table of n, a(n) for n = 1..10000</a>
%F Dirichlet g.f.: zeta(s)*zeta(s-6)/zeta(2s-6). - _R. J. Mathar_, Apr 12 2011
%F If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(6*k_j)). - _Ilya Gutkovskiy_, Nov 04 2018
%F Sum_{k=1..n} a(k) ~ 1350*Zeta(7)*n^7 / Pi^8. - _Vaclav Kotesovec_, Feb 07 2019
%t Total[#^6]&/@Table[Select[Divisors[n],GCD[#,n/#]==1&],{n,30}] (* _Harvey P. Dale_, Jul 17 2011 *)
%t a[1] = 1; a[n_] := Times @@ (1 + First[#]^(6*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* _Amiram Eldar_, Aug 10 2019 *)
%Y Cf. A034444, A034448.
%Y Row n=6 of A286880.
%K nonn,mult
%O 1,2
%A _Erich Friedman_
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