A307837 a(1) = 1; a(n+1) = Sum_{d|n} lambda(d)*a(d), where lambda = Liouville function (A008836).

1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 0, -1, -1, -1, 2, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 1, 2, 1, 0, 1, 0, 2, -1, -2, 3, -3, -2, 1, 1, -1, 2, 3, 3, 2, 3, 3, -2, -3, 4, 4, -3, -3, -3, 4, -3, 4, 4, -3, 4, -5, 6, 6, -6, 8, 9, -9, 10, -8, -6, -7, 8, 7, 6, 5, 6, 7, -6, -8, -7, 6, 7, 9, 9, 5, -4, 2, -1

Offset: 1

Author

Ilya Gutkovskiy, May 01 2019

Keywords

• sign

Crossrefs

Cf. A001222, A008836, A061020, A070965, A206369.

Programs

Mathematica

a[n_] := a[n] = Sum[LiouvilleLambda[d] a[d], {d, Divisors[n - 1]}]; a[1] = 1; Table[a[n], {n, 1, 100}]
a[n_] := a[n] = SeriesCoefficient[x (1 + Sum[LiouvilleLambda[k] a[k] x^k/(1 - x^k), {k, 1, n - 1}]), {x, 0, n}]; Table[a[n], {n, 1, 100}]

Formula

G.f.: x * (1 + Sum_{n>=1} lambda(n)*a(n)*x^n/(1 - x^n)).