A307421 Dirichlet g.f.: zeta(s) * zeta(3*s) / zeta(2*s).

1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1

Offset

1

Comments

Dirichlet convolution of A008966 and A010057.

Links

Vaclav Kotesovec, Table of n, a(n) for n = 1..10000

Vaclav Kotesovec, Graph - the asymptotic ratio.

Eric Weisstein's World of Mathematics, Dirichlet Generating Function.

Wikipedia, Dirichlet series.

Formula

a(n) = abs(A210826(n)).

Sum_{k=1..n} a(k) ~ 6*zeta(3)*n/Pi^2 + zeta(1/3)*n^(1/3)/zeta(2/3).

Multiplicative with a(p^e) = 0 if e == 2 (mod 3), and 1 otherwise. - Amiram Eldar, Dec 25 2022

Mathematica

Table[DivisorSum[n, Boole[IntegerQ[#^(1/3)]] * Abs[MoebiusMu[n/#]]&], {n, 1, 100}]
f[p_, e_] := If[Mod[e, 3] == 2, 0, 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)/(1-X^3))[n], ", ")) \\ Vaclav Kotesovec, Jun 14 2020

Crossrefs

Cf. A010057, A008966, A210826, A299406.

Sequence in context: A014677 A307425 A210826 * A299406 A287769 A267866

Adjacent sequences: A307418 A307419 A307420 * A307422 A307423 A307424

Keyword

nonn,mult

Author

Vaclav Kotesovec, Apr 08 2019

Status

approved