A034678 Sum of fourth powers of unitary divisors.

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

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