A346034 a(1) = 1, a(2) = 0; a(n+2) = Sum_{d|n} mu(n/d) * a(d).

1, 0, 1, -1, 0, -1, -1, -1, -2, 0, -3, 1, -4, 3, -5, 5, -5, 6, -6, 10, -7, 11, -6, 15, -7, 14, -7, 19, -5, 17, -6, 23, -7, 18, -4, 24, -2, 16, -3, 23, 1, 13, 0, 17, -1, 7, 7, 14, 6, -7, 7, 0, 12, -13, 11, -14, 15, -33, 21, -27, 20, -57, 19, -50, 29, -73, 34, -79, 33, -96

Offset: 1

Author

Ilya Gutkovskiy, Jul 01 2021

Keywords

• sign

Crossrefs

Cf. A007439, A007554, A008683, A318583, A345138, A345141.

Programs

Mathematica

a[1] = 1; a[2] = 0; a[n_] := a[n] = Sum[MoebiusMu[(n - 2)/d] a[d], {d, Divisors[n - 2]}]; Table[a[n], {n, 1, 70}]
nmax = 70; A[] = 0; Do[A[x] = x + x^2 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 + x^2 * Sum_{k>=1} mu(k) * A(x^k).