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A051002 Sum of 5th powers of odd divisors of n. 14
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

J. W. L. Glaisher, On the representations of a number as the sum of two, four, six, eight, ten, and twelve squares, Quart. J. Math. 38 (1907), 1-62 (see p. 4 and p. 8).

Eric Weisstein's World of Mathematics, Odd Divisor Function

Index entries for sequences mentioned by Glaisher

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 January 15 20:47 EST 2019. Contains 319184 sequences. (Running on oeis4.)