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A285989 a(0) = 0, a(n) = Sum_{0<d|n, n/d odd} d^4 for n > 0. 5
0, 1, 16, 82, 256, 626, 1312, 2402, 4096, 6643, 10016, 14642, 20992, 28562, 38432, 51332, 65536, 83522, 106288, 130322, 160256, 196964, 234272, 279842, 335872, 391251, 456992, 538084, 614912, 707282, 821312, 923522, 1048576, 1200644, 1336352, 1503652, 1700608 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Multiplicative because this sequence is the Dirichlet convolution of A000035 and A000583 which are both multiplicative. - Andrew Howroyd, Aug 05 2018

LINKS

Robert Israel, Table of n, a(n) for n = 0..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).

Index entries for sequences mentioned by Glaisher

FORMULA

a(n) = A051001(n)*16^A007814(n) for n >= 1. - Robert Israel, Apr 30 2017

MAPLE

f:= n -> add((n/d)^4, d = numtheory:-divisors(n/2^padic:-ordp(n, 2))); # Robert Israel, Apr 30 2017

MATHEMATICA

{0}~Join~Table[DivisorSum[n, Mod[#, 2] (n/#)^4 &], {n, 36}] (* Michael De Vlieger, Aug 05 2018 *)

PROG

(PARI) a(n)={sumdiv(n, d, (d%2)*(n/d)^4)} \\ Andrew Howroyd, Aug 05 2018

CROSSREFS

Sum_{0<d|n, n/d odd} d^k: A002131 (k=1), A076577 (k=2), A007331 (k=3), this sequence (k=4), A096960 (k=5), A096961 (k=7), A096962 (k=9), A096963 (k=11).

Cf. A000035, A000583, A007814, A051001, A206623, A285990.

Sequence in context: A151502 A030693 A308249 * A231303 A218082 A159501

Adjacent sequences:  A285986 A285987 A285988 * A285990 A285991 A285992

KEYWORD

nonn,mult

AUTHOR

Seiichi Manyama, Apr 30 2017

STATUS

approved

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Last modified May 12 01:49 EDT 2021. Contains 343808 sequences. (Running on oeis4.)