A346118 a(1) = 1; a(n+1) = 1 + Sum_{d|n} mu(n/d) * a(d).

1, 2, 2, 2, 1, 1, -1, -1, -2, -3, -4, -4, -4, -4, -3, -4, -2, -2, 2, 2, 6, 7, 11, 11, 19, 19, 23, 26, 31, 31, 41, 41, 46, 50, 52, 54, 62, 62, 60, 64, 66, 66, 66, 66, 60, 68, 57, 57, 50, 52, 38, 40, 22, 22, 0, 5, -17, -19, -50, -50, -80, -80, -121, -122, -162, -157, -211, -211, -260, -271

Offset: 1

Author

Ilya Gutkovskiy, Jul 05 2021

Keywords

• sign

Crossrefs

Cf. A007554, A008683, A067824, A068336, A317581.

Programs

Mathematica

a[1] = 1; a[n_] := a[n] = 1 + Sum[MoebiusMu[(n - 1)/d] a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 70}]
nmax = 70; A[] = 0; Do[A[x] = x (1/(1 - x) + Sum[MoebiusMu[k] A[x^k], {k, 1, nmax}]) + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] // Rest

Formula

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