OFFSET
1,3
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
a(n) = a(A000265(n)). - M. F. Hasler, Nov 26 2018
G.f.: Sum_{k>=1} (-1)^(k-1)*(2*k - 1)^12*x^(2*k-1)/(1 - x^(2*k-1)). - Ilya Gutkovskiy, Dec 22 2018
Multiplicative with a(2^e) = 1, and for an odd prime p, ((p^12)^(e+1)-1)/(p^12-1) if p == 1 (mod 4) and ((-p^12)^(e+1)-1)/(-p^12-1) if p == 3 (mod 4). - Amiram Eldar, Sep 27 2023
a(n) = Sum_{d|n} d^12*sin(d*Pi/2). - Ridouane Oudra, Sep 08 2024
MATHEMATICA
s[n_, r_] := DivisorSum[n, #^12 &, Mod[#, 4] == r &]; a[n_] := s[n, 1] - s[n, 3]; Array[a, 30] (* Amiram Eldar, Nov 26 2018 *)
f[p_, e_] := If[Mod[p, 4] == 1, ((p^12)^(e+1)-1)/(p^12-1), ((-p^12)^(e+1)-1)/(-p^12-1)]; f[2, e_] := 1; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 60] (* Amiram Eldar, Sep 27 2023 *)
PROG
(PARI) apply( A321828(n)=sumdiv(n>>valuation(n, 2), d, (2-d%4)*d^12), [1..40]) \\ M. F. Hasler, Nov 26 2018
CROSSREFS
KEYWORD
sign,easy,mult
AUTHOR
N. J. A. Sloane, Nov 24 2018
STATUS
approved