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

1,2

Links

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

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

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 *)

Crossrefs

Cf. A034444, A034448.

Row n=8 of A286880.

Sequence in context: A351271 A155468 A321564 * A351303 A017679 A013956

Adjacent sequences: A034679 A034680 A034681 * A034683 A034684 A034685

Keyword

nonn,mult

Author

Erich Friedman

Status

approved