A338639 a(0) = 1; for n > 0, a(n) = -Sum_{d|n, d < n} a(d - 1).

1, 0, -1, -1, -1, -1, 0, -1, 0, 0, 0, -1, 2, -1, -1, 1, 1, -1, 1, -1, 1, 0, -1, -1, 4, 0, -3, 0, 1, -1, 3, -1, 0, 0, -2, 0, 4, -1, -2, -2, 3, -1, 1, -1, 0, 2, 0, -1, 4, -1, -4, -1, -2, -1, 5, 0, 2, -1, -2, -1, 7, -1, -4, -1, 1, -2, 1, -1, -1, 1, 3, -1, 6, -1, -5, -2, 0, -1, 1, -1, 4

Offset: 0

Author

Ilya Gutkovskiy, Nov 05 2020

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A167865, A281487, A308077, A343371.

Programs

Mathematica

a[0] = 1; a[n_] := a[n] = -DivisorSum[n, a[# - 1] &, # < n &]; Table[a[n], {n, 0, 80}]
nmax = 80; A[] = 0; Do[A[x] = 1 - Sum[x^k A[x^k], {k, 2, nmax}] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]

Formula

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