A338656 a(n) = Sum_{d|n} mu(d) * binomial(d + n/d - 2, d-1).

1, 0, 0, -1, 0, -4, 0, -3, -5, -8, 0, -9, 0, -12, -28, -7, 0, -8, 0, -34, -54, -20, 0, 9, -69, -24, -44, -83, 0, 0, 0, -15, -130, -32, -418, 157, 0, -36, -180, -129, 0, 0, 0, -285, -494, -44, 0, 633, -923, -24, -304, -454, 0, 1090, -2000, -1183, -378, -56, 0, 3050, 0, -60, -3002, -31, -3638, 0

Offset: 1

Author

Seiichi Manyama, Apr 22 2021

Keywords

• sign
• look

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A008683, A157020, A332470, A338657.

Programs

Mathematica

a[n_] := DivisorSum[n, MoebiusMu[#] * Binomial[# + n/# - 2, # - 1] &]; Array[a, 100] (* Amiram Eldar, Apr 22 2021 *)

PARI

a(n) = sumdiv(n, d, moebius(d)*binomial(d+n/d-2, d-1));

PARI

my(N=66, x='x+O('x^N)); Vec(sum(k=1, N, moebius(k)*(x/(1-x^k))^k))

Formula

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

If p is prime, a(p) = 0.