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 A034678 Sum of fourth powers of unitary divisors. 3

%I

%S 1,17,82,257,626,1394,2402,4097,6562,10642,14642,21074,28562,40834,

%T 51332,65537,83522,111554,130322,160882,196964,248914,279842,335954,

%U 390626,485554,531442,617314,707282,872644,923522,1048577,1200644

%N Sum of fourth powers of unitary divisors.

%H Amiram Eldar, <a href="/A034678/b034678.txt">Table of n, a(n) for n = 1..10000</a>

%F Dirichlet g.f.: zeta(s)*zeta(s-4)/zeta(2*s-4). - _R. J. Mathar_, Mar 04 2011

%F If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(4*k_j)). - _Ilya Gutkovskiy_, Nov 04 2018

%F Sum_{k=1..n} a(k) ~ 189 * Zeta(5) * n^5 / Pi^6. - _Vaclav Kotesovec_, Feb 01 2019

%t Table[Total[Select[Divisors[n], CoprimeQ[#, n/#] &]^4], {n, 1, 50}] (* _Vaclav Kotesovec_, Feb 01 2019 *)

%t a[1] = 1; a[n_] := Times @@ (1 + First[#]^(4*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* _Amiram Eldar_, Aug 10 2019 *)

%o (PARI) A000012=direuler(p=2,119, 1/(1-X)) ;

%o A000583=direuler(p=2,119, 1/(1-p^4*X)) ;

%o A000290x=direuler(p=2,119, 1-p^4*X^2) ;

%o dirmul(dirmul(A000012,A000583),A000290x) /* _R. J. Mathar_, Mar 05 2011 */

%Y Cf. A034444, A034448.

%Y Row n=4 of A286880.

%K nonn,mult

%O 1,2

%A _Erich Friedman_

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Last modified December 10 21:53 EST 2019. Contains 329909 sequences. (Running on oeis4.)