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 A051000 Sum of cubes of odd divisors of n. 18
 1, 1, 28, 1, 126, 28, 344, 1, 757, 126, 1332, 28, 2198, 344, 3528, 1, 4914, 757, 6860, 126, 9632, 1332, 12168, 28, 15751, 2198, 20440, 344, 24390, 3528, 29792, 1, 37296, 4914, 43344, 757, 50654, 6860, 61544, 126, 68922, 9632, 79508, 1332, 95382 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The sum of cubes of even divisors of 2*k equals 8*A001158(k), and the sum of cubes of even divisors of 2*k-1 vanishes, for k >= 1. - Wolfdieter Lang, Jan 07 2017 LINKS Reinhard Zumkeller, 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^(3-s))*zeta(s)*zeta(s-3). Dirichlet convolution of (-1)^n*A176415(n) and A000578. - R. J. Mathar, Apr 06 2011 a(n) = Sum_{k=1..A001227(n)} A182469(n,k)^3. - Reinhard Zumkeller, May 01 2012 G.f.: Sum_{k>=1} (2*k - 1)^3*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Jan 04 2017 MATHEMATICA Table[Total[Select[Divisors[n], OddQ]^3], {n, 50}] (* Harvey P. Dale, Jun 28 2012 *) PROG (Haskell) a051000 = sum . map (^ 3) . a182469_row -- Reinhard Zumkeller, May 01 2012 (PARI) a(n) = sumdiv(n, d, (d%2)*d^3); \\ Michel Marcus, Jan 04 2017 CROSSREFS Cf. A000593, A001227, A001158, A050999, A051001, A051002. Sequence in context: A040809 A040810 A040811 * A132057 A292919 A040777 Adjacent sequences:  A050997 A050998 A050999 * A051001 A051002 A051003 KEYWORD nonn,mult AUTHOR STATUS approved

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Last modified January 22 01:29 EST 2019. Contains 319351 sequences. (Running on oeis4.)