A354359 Dirichlet inverse of A124859.

1, -2, -2, -2, -2, 4, -2, -14, -2, 4, -2, 4, -2, 4, 4, -110, -2, 4, -2, 4, 4, 4, -2, 28, -2, 4, -14, 4, -2, -8, -2, -1526, 4, 4, 4, 4, -2, 4, 4, 28, -2, -8, -2, 4, 4, 4, -2, 220, -2, 4, 4, 4, -2, 28, 4, 28, 4, 4, -2, -8, -2, 4, 4, -20858, 4, -8, -2, 4, 4, -8, -2, 28, -2, 4, 4, 4, 4, -8, -2, 220, -110, 4, -2, -8

Offset: 1

Author

Antti Karttunen, Jun 05 2022

Keywords

• sign
• mult

Comments

Multiplicative because A124859 is.

Links

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

Crossrefs

Cf. A002110, A124859.

Cf. also A354186, A354349, A354351, A354358.

Programs

PARI

A124859(n) = { my(f=factor(n)); for(k=1, #f~, f[k, 1] = prod(j=1, f[k, 2], prime(j)); f[k, 2] = 1); factorback(f); }; \\ From A124859
memoA354359 = Map();
A354359(n) = if(1==n,1,my(v); if(mapisdefined(memoA354359,n,&v), v, v = -sumdiv(n,d,if(dA124859(n/d)*A354359(d),0)); mapput(memoA354359,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d < n} A124859(n/d) * a(d).