|
%I #19 Dec 25 2022 02:11:53
%S 1,0,0,-1,0,0,0,1,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,1,0,0,0,0,-1,
%T 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,
%U 0,0,0,0,0,-1,0,0,0,0,0,0,0,0,0,0,0,0,0
%N Dirichlet g.f.: zeta(3*s) / zeta(2*s).
%C Dirichlet convolution of A210826 and A008966.
%C Dirichlet convolution of A271102 and A010057.
%H Vaclav Kotesovec, <a href="/A307424/b307424.txt">Table of n, a(n) for n = 1..10000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DirichletGeneratingFunction.html">Dirichlet Generating Function</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Dirichlet_series">Dirichlet series</a>.
%F 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
%t Table[DivisorSum[n, Abs[MoebiusMu[#]] * Mod[DivisorSigma[0, n/#], 3, -1]&], {n, 1, 100}]
%t 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 *)
%o (PARI) for(n=1, 100, print1(direuler(p=2, n, (1-X^2)/(1-X^3))[n], ", ")) \\ _Vaclav Kotesovec_, Jun 14 2020
%Y Cf. A008966, A010057, A210826, A271102, A307423.
%K sign,mult
%O 1
%A _Vaclav Kotesovec_, Apr 08 2019
|
