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} (-1)^(k-1)*k^8*x^k/(1 - x^k). - Ilya Gutkovskiy, Dec 23 2018
Multiplicative with a(2^e) = 2 - (2^(8*e + 8) - 1)/255, and a(p^e) = (p^(8*e + 8) - 1)/(p^8 - 1) for p > 2. - Amiram Eldar, Nov 04 2022
MATHEMATICA
f[p_, e_] := (p^(8*e + 8) - 1)/(p^8 - 1); f[2, e_] := 2 - (2^(8*e + 8) - 1)/255; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 24] (* Amiram Eldar, Nov 04 2022 *)
PROG
(PARI) apply( a(n)=sumdiv(n, d, (-1)^(d-1)*d^8), [1..30]) \\ M. F. Hasler, Nov 26 2018
CROSSREFS
KEYWORD
sign,mult
AUTHOR
N. J. A. Sloane, Nov 23 2018
STATUS
approved