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A051002 Sum of 5th powers of odd divisors of n. 7
1, 1, 244, 1, 3126, 244, 16808, 1, 59293, 3126, 161052, 244, 371294, 16808, 762744, 1, 1419858, 59293, 2476100, 3126, 4101152, 161052, 6436344, 244, 9768751, 371294, 14408200, 16808, 20511150, 762744, 28629152, 1, 39296688, 1419858 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

REFERENCES

T. M. Apostol, Modular Functions and Dirichlet Series in Number Theory, Springer-Verlag, 1990, page 25, Exercise 15 (corrected).

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Odd Divisor Function

FORMULA

Dirichlet g.f. (1-2^(5-s))*zeta(s)*zeta(s-5). - R. J. Mathar, Apr 06 2011

G.f.: Sum_{k>=1} (2*k - 1)^5*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Jan 04 2017

The preceding g.f. is also 34*sigma_5(x^2) - 64*sigma_5(x^4) - sigma_5(-x), with sigma_5 the g.f. of A001160. Compare this with the Apostol reference which gives the g.f. of a(n)*(-1)^(n+1). - Wolfdieter Lang, Jan 31 2017

MATHEMATICA

a[n_] := Select[ Divisors[n], OddQ]^5 // Total; Table[a[n], {n, 1, 34}] (* Jean-Fran├žois Alcover, Oct 25 2012 *)

PROG

(PARI) a(n) = sumdiv(n , d, (d%2)*d^5); \\ Michel Marcus, Jan 14 2014

CROSSREFS

Cf. A000593, A001227, A050999, A051000, A051001, A001160.

Sequence in context: A151638 A248137 A243774 * A044987 A201998 A234262

Adjacent sequences:  A050999 A051000 A051001 * A051003 A051004 A051005

KEYWORD

nonn,mult

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified October 18 04:14 EDT 2018. Contains 316304 sequences. (Running on oeis4.)