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A034682 Sum of eighth powers of unitary divisors. 3
1, 257, 6562, 65537, 390626, 1686434, 5764802, 16777217, 43046722, 100390882, 214358882, 430053794, 815730722, 1481554114, 2563287812, 4294967297, 6975757442, 11063007554, 16983563042, 25600456162, 37828630724 (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-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: A125648 A155468 A321564 * A017679 A013956 A294303

Adjacent sequences:  A034679 A034680 A034681 * A034683 A034684 A034685

KEYWORD

nonn,mult

AUTHOR

Erich Friedman

STATUS

approved

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Last modified December 6 14:15 EST 2019. Contains 329806 sequences. (Running on oeis4.)