A355692 Dirichlet inverse of A355442, gcd(A003961(n), A276086(n)), where A003961 is fully multiplicative with a(p) = nextprime(p), and A276086 is primorial base exp-function.

1, -3, -1, 0, -1, 1, -1, 24, -4, 3, -1, 16, -1, 3, -3, -72, -1, 6, -1, 6, -3, 3, -1, -68, 0, 3, -116, 0, -1, 21, -1, 24, 1, 3, -5, 72, -1, 3, -3, -120, -1, 23, -1, 6, -158, 3, -1, 28, 0, -18, -3, 0, -1, 632, -5, -24, -3, 3, -1, -54, -1, 3, 16, 504, -5, -1, -1, 6, -3, 15, -1, -400, -1, 3, -236, 0, 1, 23, -1, 474, 136

Offset: 1

Author

Antti Karttunen, Jul 18 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..11550
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences computed from indices in prime factorization
• Index entries for sequences related to primorial base

Crossrefs

Cf. A003961, A276086.

Cf. also A346242, A354347, A354348, A354823, A354824.

Programs

PARI

A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A355442(n) = gcd(A003961(n), A276086(n));
memoA355692 = Map();
A355692(n) = if(1==n,1,my(v); if(mapisdefined(memoA355692,n,&v), v, v = -sumdiv(n,d,if(dA355442(n/d)*A355692(d),0)); mapput(memoA355692,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA355442(n/d) * a(d).