OFFSET
1,2
LINKS
Seiichi Manyama, 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).
FORMULA
G.f.: Sum_{k>=1} k^12*x^k/(1 - x^(2*k)). - Ilya Gutkovskiy, Dec 22 2018
From Amiram Eldar, Nov 02 2022: (Start)
Multiplicative with a(2^e) = 2^(12*e) and a(p^e) = (p^(12*e+12)-1)/(p^12-1) for p > 2.
Sum_{k=1..n} a(k) ~ c * n^13, where c = 8191*zeta(13)/106496 = 0.0769231... . (End)
Dirichlet g.f.: zeta(s)*zeta(s-12)*(1-1/2^s). - Amiram Eldar, Jan 09 2023
MATHEMATICA
a[n_] := DivisorSum[n, #^12 &, OddQ[n/#] &]; Array[a, 20] (* Amiram Eldar, Nov 02 2022 *)
PROG
(PARI) apply( A321820(n)=sumdiv(n, d, if(bittest(n\d, 0), d^12)), [1..30]) \\ M. F. Hasler, Nov 26 2018
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
N. J. A. Sloane, Nov 24 2018
STATUS
approved