A343493 a(n) = 1 - Sum_{d|n, d < n} a(d - 1).

1, 1, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, -1, 0, 0, 1, -1, 0, 0, 0, 0, 1, -1, 0, -1, 1, 0, 1, 0, 0, 0, 0, -2, 0, 0, 2, 0, 0, -1, 1, 0, 0, 0, 0, -2, 2, 0, 0, -2, 1, 1, 1, -1, 0, 0, 1, -1, 0, -1, 0, 0, 0, -1, 2, -2, 2, 0, 0, 0, 1, 1, 0, -2, 0, -1, 2, -1, 1, 0, 0, -2, 1, -1, 0, -1, 2, -1, 0, -2, 0, 3

Offset: 0

Author

Ilya Gutkovskiy, Apr 17 2021

Keywords

• sign

Crossrefs

Cf. A167865, A281487, A338639, A343371.

Programs

Mathematica

a[n_] := a[n] = 1 - Sum[If[d < n, a[d - 1], 0], {d, Divisors[n]}]; Table[a[n], {n, 0, 90}]
nmax = 90; A[] = 0; Do[A[x] = 1/(1 - x) - Sum[x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) //Normal, nmax + 1]; CoefficientList[A[x], x]

Python

from functools import lru_cache
from sympy import divisors
@lru_cache(maxsize=None)
def A343493(n): return 1-sum(A343493(d-1) for d in divisors(n) if d < n) # Chai Wah Wu, Apr 17 2021

Formula

G.f. A(x) satisfies: A(x) = 1 / (1 - x) - x^2 * A(x^2) - x^3 * A(x^3) - x^4 * A(x^4) - ...