A354349 Dirichlet inverse of A181819, prime shadow of n.

1, -2, -2, 1, -2, 4, -2, -1, 1, 4, -2, -2, -2, 4, 4, 2, -2, -2, -2, -2, 4, 4, -2, 2, 1, 4, -1, -2, -2, -8, -2, -3, 4, 4, 4, 1, -2, 4, 4, 2, -2, -8, -2, -2, -2, 4, -2, -4, 1, -2, 4, -2, -2, 2, 4, 2, 4, 4, -2, 4, -2, 4, -2, 7, 4, -8, -2, -2, 4, -8, -2, -1, -2, 4, -2, -2, 4, -8, -2, -4, 2, 4, -2, 4, 4, 4, 4, 2, -2, 4, 4

Offset: 1

Author

Antti Karttunen, Jun 05 2022

Keywords

• sign
• mult

Comments

Multiplicative because A181819 is.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A181819.

Cf. also A354186, A354351, A354359.

Programs

PARI

A181819(n) = factorback(apply(e->prime(e),(factor(n)[,2])));
memoA354349 = Map();
A354349(n) = if(1==n,1,my(v); if(mapisdefined(memoA354349,n,&v), v, v = -sumdiv(n,d,if(dA181819(n/d)*A354349(d),0)); mapput(memoA354349,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A181819(n/d) * a(d).