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).
FORMULA
From Amiram Eldar, Nov 01 2022: (Start)
Multiplicative with a(2^e) = 2^(4*e) and a(p^e) = (p^(4*e+4)-1)/(p^4-1) for p > 2.
Sum_{k=1..n} a(k) ~ c * n^5, where c = 31*zeta(5)/160 = 0.200904... . (End)
Dirichlet g.f.: zeta(s)*zeta(s-4)*(1-1/2^s). - Amiram Eldar, Jan 08 2023
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
KEYWORD
nonn,mult
AUTHOR
Seiichi Manyama, Apr 30 2017
STATUS
approved