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

Author

Erich Friedman

Keywords

• nonn
• mult

Links

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

Crossrefs

Cf. A034444, A034448.

Row n=4 of A286880.

Programs

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 *)

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 */

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