A307424 Dirichlet g.f.: zeta(3*s) / zeta(2*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, 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, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1

Comments

Dirichlet convolution of A210826 and A008966.

Dirichlet convolution of A271102 and A010057.

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

Cf. A008966, A010057, A210826, A271102, A307423.

Sequence in context: A252488 A170956 A293449 * A355448 A354868 A075802

Adjacent sequences: A307421 A307422 A307423 * A307425 A307426 A307427

Keyword

sign,mult

Author

Vaclav Kotesovec, Apr 08 2019

Status

approved