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A051001 Sum of 4th powers of odd divisors of n. 16
1, 1, 82, 1, 626, 82, 2402, 1, 6643, 626, 14642, 82, 28562, 2402, 51332, 1, 83522, 6643, 130322, 626, 196964, 14642, 279842, 82, 391251, 28562, 538084, 2402, 707282, 51332, 923522, 1, 1200644, 83522, 1503652, 6643, 1874162, 130322 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Robert Israel, 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^(4-s))*zeta(s)*zeta(s-4). - R. J. Mathar, Apr 06 2011

G.f.: Sum_{k>=1} (2*k - 1)^4*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Jan 04 2017

a(n) = A001159(A000265(n)). - Robert Israel, Jan 05 2017

MAPLE

f:= proc(n) add(x^4, x = numtheory:-divisors(n/2^padic:-ordp(n, 2))) end proc:

map(f, [$1..100]); # Robert Israel, Jan 05 2017

MATHEMATICA

Table[Total[Select[Divisors[n], OddQ]^4], {n, 40}] (* Harvey P. Dale, Oct 02 2014 *)

PROG

(PARI) a(n) = sumdiv(n , d, (d%2)*d^4); \\ Michel Marcus, Jan 14 2014

CROSSREFS

Cf. A000265, A000593, A001227, A001159, A050999, A051000, A051002.

Sequence in context: A116268 A128838 A231484 * A033402 A143757 A038008

Adjacent sequences:  A050998 A050999 A051000 * A051002 A051003 A051004

KEYWORD

nonn,mult,look

AUTHOR

Eric W. Weisstein

STATUS

approved

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Last modified January 22 16:29 EST 2020. Contains 331152 sequences. (Running on oeis4.)