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A034678 Sum of fourth powers of unitary divisors. 3
1, 17, 82, 257, 626, 1394, 2402, 4097, 6562, 10642, 14642, 21074, 28562, 40834, 51332, 65537, 83522, 111554, 130322, 160882, 196964, 248914, 279842, 335954, 390626, 485554, 531442, 617314, 707282, 872644, 923522, 1048577, 1200644 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..10000

FORMULA

Dirichlet g.f.: zeta(s)*zeta(s-4)/zeta(2*s-4). - R. J. Mathar, Mar 04 2011

If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(4*k_j)). - Ilya Gutkovskiy, Nov 04 2018

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

MATHEMATICA

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

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

PROG

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

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

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

dirmul(dirmul(A000012, A000583), A000290x) /* R. J. Mathar, Mar 05 2011 */

CROSSREFS

Cf. A034444, A034448.

Row n=4 of A286880.

Sequence in context: A184982 A088687 A321560 * A065960 A017671 A001159

Adjacent sequences:  A034675 A034676 A034677 * A034679 A034680 A034681

KEYWORD

nonn,mult

AUTHOR

Erich Friedman

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)