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A096960 Sum_{0<d|n, n/d odd} d^5. 10
1, 32, 244, 1024, 3126, 7808, 16808, 32768, 59293, 100032, 161052, 249856, 371294, 537856, 762744, 1048576, 1419858, 1897376, 2476100, 3201024, 4101152, 5153664, 6436344, 7995392, 9768751, 11881408, 14408200, 17211392, 20511150 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Seiichi Manyama, Table of n, a(n) for n = 1..10000

H. H. Chan and C. Krattenthaler, Recent progress in the study of representations of integers as sums of squares, arXiv:math/0407061 [math.NT], 2004.

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).

Index entries for sequences mentioned by Glaisher

FORMULA

G.f.: Sum {k>0} k^5 * x^k / (1 - x^(2*k)).

EXAMPLE

G.f. = q + 32*q^2 + 244*q^3 + 1024*q^4 + 3126*q^5 + 7808*q^6 + 16808*q^7 + 32768*q^8 + ...

MATHEMATICA

a[ n_] := If[ n < 1, 0, Sum[ d^5 Boole[ OddQ[ n/d]], {d, Divisors[ n]}]]; (* Michael Somos, Jun 04 2013 *)

a[ n_] := SeriesCoefficient[ (EllipticTheta[ 3, 0, q]^4 + EllipticTheta[ 2, 0, q]^4) EllipticTheta[ 2, 0, q^(1/2)]^8 / 256, {q, 0, n}]; (* Michael Somos, Jun 04 2013 *)

PROG

(PARI) {a(n) = if( n<1, 0, sumdiv( n, d, (n/d%2) * d^5))};

(Sage) ModularForms( Gamma0(2), 6, prec=33).2; # Michael Somos, Jun 04 2013

(MAGMA) Basis( ModularForms( Gamma0(2), 6), 30) [2]; /* Michael Somos, Nov 30 2014 */

CROSSREFS

Cf. A007331, A096961, A096962, A096963.

Sequence in context: A050997 A056572 A226098 * A231304 A269079 A134846

Adjacent sequences:  A096957 A096958 A096959 * A096961 A096962 A096963

KEYWORD

nonn,mult

AUTHOR

Ralf Stephan, Jul 18 2004

STATUS

approved

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Last modified January 15 18:44 EST 2019. Contains 319162 sequences. (Running on oeis4.)