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

1,2

Links

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

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.

Mathematica

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

Prog

(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)))

Crossrefs

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

Sequence in context: A231563 A282849 A111813 * A362208 A167156 A132952

Adjacent sequences: A346770 A346771 A346772 * A346774 A346775 A346776

Keyword

nonn,easy

Author

Seiichi Manyama, Aug 03 2021

Status

approved