A346482 Dirichlet inverse of A005171, the characteristic function of nonprimes.

1, 0, 0, -1, 0, -1, 0, -1, -1, -1, 0, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, -1, 0, 1, -1, -1, -1, -1, 0, -1, 0, 1, -1, -1, -1, 2, 0, -1, -1, 1, 0, -1, 0, -1, -1, -1, 0, 3, -1, -1, -1, -1, 0, 1, -1, 1, -1, -1, 0, 3, 0, -1, -1, 1, -1, -1, 0, -1, -1, -1, 0, 5, 0, -1, -1, -1, -1, -1, 0, 3, 0, -1, 0, 3, -1, -1, -1, 1, 0, 3

Offset: 1

Author

Mats Granvik and Antti Karttunen, Aug 17 2021

Keywords

• sign

Comments

In addition to A168645, -1's occur also in the following positions: 256, 512, 6561, 16384, 19683, 32768, 390625, 1048576, ...

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A005171, A010051, A018252, A168645, A346483.

Union of A000040 and A346484 gives the positions of zeros.

Programs

PARI

up_to = 65537;
DirInverseCorrect(v) = { my(u=vector(#v)); u[1] = (1/v[1]); for(n=2, #v, u[n] = (-u[1]*sumdiv(n, d, if(dA005171(n) = (1-isprime(n));
v346482 = DirInverseCorrect(vector(up_to,n,A005171(n)));
A346482(n) = v346482[n];

Formula

a(1) = 1; and for n > 2, a(n) = -Sum_{d|n, dA005171(n/d).

a(n) = A346483(n) - A005171(n).