OFFSET
1
COMMENTS
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Dirichlet Generating Function.
Wikipedia, Dirichlet series.
FORMULA
Multiplicative with a(p^e) = 1 if e == 0 (mod 3), 0 if e == 1 (mod 3), and -1 if e == 2 (mod 3). - Amiram Eldar, Dec 25 2022
MATHEMATICA
Table[DivisorSum[n, Abs[MoebiusMu[#]] * Mod[DivisorSigma[0, n/#], 3, -1]&], {n, 1, 100}]
f[p_, e_] := Switch[Mod[e, 3], 0, 1, 1, 0, 2, -1]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Dec 25 2022 *)
PROG
(PARI) for(n=1, 100, print1(direuler(p=2, n, (1-X^2)/(1-X^3))[n], ", ")) \\ Vaclav Kotesovec, Jun 14 2020
CROSSREFS
KEYWORD
sign,mult
AUTHOR
Vaclav Kotesovec, Apr 08 2019
STATUS
approved