A346773 a(n) = Sum_{d|n} möbius(d)^n.

1, 2, 0, 2, 0, 4, 0, 2, 0, 4, 0, 4, 0, 4, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 2, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 2, 0, 8, 0, 4, 0, 8, 0, 4, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, 0, 8, 0, 4, 0, 4, 0, 4, 0, 4, 0, 4, 0, 8, 0

Offset: 1

Author

Seiichi Manyama, Aug 03 2021

Keywords

• nonn
• easy

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A008683, A023887, A034444, A068068, A080323, A100008, A264782.

Programs

Mathematica

Table[Sum[MoebiusMu[d]^n,{d,Divisors[n]}],{n,103}] (* Stefano Spezia, Aug 03 2021 *)

PARI

a(n) = sumdiv(n, d, moebius(d)^n);

PARI

a(n) = if(n%2, 0^(n-1), 2^omega(2*n));

PARI

N=99; x='x+O('x^N); Vec(sum(k=1, N, (moebius(k)*x)^k/(1-(moebius(k)*x)^k)))

Formula

G.f.: Sum_{k>=1} (mu(k)*x)^k/(1 - (mu(k)*x)^k).

a(2*n-1) = 0^(n-1) and a(2*n) = A034444(2*n) = A100008(n) for n > 0.