A334743 a(1) = 1; a(n) = -Sum_{d|n, d < n} omega(n/d) * a(d), where omega = A001221.

1, -1, -1, 0, -1, 0, -1, 0, 0, 0, -1, 1, -1, 0, 0, 0, -1, 1, -1, 1, 0, 0, -1, 0, 0, 0, 0, 1, -1, 3, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 3, -1, 1, 1, 0, -1, 0, 0, 1, 0, 1, -1, 0, 0, 0, 0, 0, -1, -1, -1, 0, 1, 0, 0, 3, -1, 1, 0, 3, -1, -1, -1, 0, 1, 1, 0, 3, -1, 0, 0, 0, -1, -1, 0, 0, 0, 0, -1, -1

Offset: 1

Author

Ilya Gutkovskiy, May 09 2020

Keywords

• sign

Comments

Dirichlet inverse of A087802. - Antti Karttunen, Nov 29 2024

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Eric Weisstein's World of Mathematics, Distinct Prime Factors

Crossrefs

Cf. A001221, A007427, A008480, A008683, A010051, A087802 (Dirichlet inverse), A327276, A334744.

Programs

Mathematica

a[n_] := If[n == 1, n, -Sum[If[d < n, PrimeNu[n/d] a[d], 0], {d, Divisors[n]}]]; Table[a[n], {n, 90}]

PARI

memoA334743 = Map();
A334743(n) = if(1==n,1,my(v); if(mapisdefined(memoA334743,n,&v), v, v = -sumdiv(n,d,if(dA334743(d),0)); mapput(memoA334743,n,v); (v))); \\ Antti Karttunen, Nov 29 2024

Formula

G.f. A(x) satisfies: A(x) = x - Sum_{k>=2} omega(k) * A(x^k).

Dirichlet g.f.: 1 / (1 + zeta(s) * primezeta(s)).