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A034680 Sum of sixth powers of unitary divisors. 2

%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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Last modified December 6 08:53 EST 2019. Contains 329788 sequences. (Running on oeis4.)