A354824 Dirichlet inverse of A351084, where A351084(n) = gcd(n, A328572(n)), and A328572 converts the primorial base expansion of n into its prime product form, but with 1 subtracted from all nonzero digits.

1, -1, -1, 0, -1, 1, -1, 0, 0, 1, -1, 0, -1, 1, -3, 0, -1, 0, -1, -4, 1, 1, -1, 0, -24, 1, 0, 0, -1, 7, -1, 0, 1, 1, 1, 0, -1, 1, 1, 8, -1, -1, -1, 0, 4, 1, -1, 0, 0, 24, 1, 0, -1, 0, -3, 0, 1, 1, -1, 4, -1, 1, -6, 0, 1, -1, -1, 0, 1, -7, -1, 0, -1, 1, 52, 0, -5, -1, -1, -8, 0, 1, -1, -6, -3, 1, 1, 0, -1, -8, -5, 0

Offset: 1

Author

Antti Karttunen, Jun 09 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..30030
• Index entries for sequences related to primorial base

Crossrefs

Cf. A351084.

Cf. also A346242, A354347, A354348, A354823.

Programs

PARI

A328572(n) = { my(m=1, p=2); while(n, if(n%p, m *= p^((n%p)-1)); n = n\p; p = nextprime(1+p)); (m); };
A351084(n) = gcd(n, A328572(n));
memoA354824 = Map();
A354824(n) = if(1==n,1,my(v); if(mapisdefined(memoA354824,n,&v), v, v = -sumdiv(n,d,if(dA351084(n/d)*A354824(d),0)); mapput(memoA354824,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA351084(n/d) * a(d).