A356154 Dirichlet inverse of A356153.

1, -1, -2, 0, -1, 3, -1, 0, 3, 1, -1, -1, -1, 1, 3, 0, -1, -7, -1, -1, 2, 1, -1, 0, -1, 1, -5, 0, -1, -5, -1, 0, 3, 1, 1, 5, -1, 1, 2, 2, -1, -3, -1, 0, -7, 1, -1, 0, -4, 2, 3, 0, -1, 15, 1, -3, 2, 1, -1, 5, -1, 1, -3, 0, 1, -5, -1, 0, 3, -1, -1, -2, -1, 1, 2, 0, -1, -3, -1, -1, 8, 1, -1, 1, 1, 1, 3, 0, -1, 17

Offset: 1

Author

Antti Karttunen, Jul 28 2022

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to primorial base

Crossrefs

Cf. A276086, A355944, A356151, A356153.

Programs

PARI

A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
A356153(n) = for(k=1, oo, if((k*A276086(k))%n==0, return(k/gcd(n,k))));
memoA356154 = Map();
A356154(n) = if(1==n,1,my(v); if(mapisdefined(memoA356154,n,&v), v, v = -sumdiv(n,d,if(dA356153(n/d)*A356154(d),0)); mapput(memoA356154,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA356153(n/d) * a(d).