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A051000 Sum of cubes of odd divisors of n. 10
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

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

Eric W. Weisstein

STATUS

approved

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Last modified October 15 13:01 EDT 2018. Contains 316236 sequences. (Running on oeis4.)