A355693 Dirichlet inverse of A330749, gcd(n, A064989(n)), where A064989 shifts the prime factorization one step towards lower primes.

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

Offset: 1

Author

Antti Karttunen, Jul 18 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences computed from indices in prime factorization

Crossrefs

Cf. A064989, A330749.

Cf. also A354365, A354366.

Programs

PARI

A330749(n) = {my(f); f = factor(n); if((n>1 && f[1, 1]==2), f[1, 2] = 0); for (i=1, #f~, f[i, 1] = precprime(f[i, 1]-1)); gcd(n, factorback(f)); };
memoA355693 = Map();
A355693(n) = if(1==n,1,my(v); if(mapisdefined(memoA355693,n,&v), v, v = -sumdiv(n,d,if(dA330749(n/d)*A355693(d),0)); mapput(memoA355693,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA330749(n/d) * a(d).