OFFSET
1
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
KEYWORD
nonn,mult
AUTHOR
Vaclav Kotesovec, Apr 08 2019
STATUS
approved