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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 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-François 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 STATUS approved

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Last modified January 25 23:08 EST 2020. Contains 331270 sequences. (Running on oeis4.)