A034682 Sum of eighth powers of unitary divisors.

1, 257, 6562, 65537, 390626, 1686434, 5764802, 16777217, 43046722, 100390882, 214358882, 430053794, 815730722, 1481554114, 2563287812, 4294967297, 6975757442, 11063007554, 16983563042, 25600456162, 37828630724

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=8 of A286880.

Programs

Mathematica

Table[Total[Select[Divisors[n], CoprimeQ[#, n/#] &]^8], {n, 1, 50}] (* Vaclav Kotesovec, Feb 07 2019 *)
a[1] = 1; a[n_] := Times @@ (1 + First[#]^(8*Last[#]) & /@ FactorInteger[n]); s = Array[a, 50] (* Amiram Eldar, Aug 10 2019 *)

Formula

Dirichlet g.f.: zeta(s)*zeta(s-8)/zeta(2s-8). - R. J. Mathar, Apr 12 2011

If n = Product (p_j^k_j) then a(n) = Product (1 + p_j^(8*k_j)). - Ilya Gutkovskiy, Nov 04 2018

Sum_{k=1..n} a(k) ~ 10395*Zeta(9)*n^9 / Pi^10. - Vaclav Kotesovec, Feb 07 2019