A354825 Dirichlet inverse of A293442, where A293442 is multiplicative with a(p^e) = A019565(e).

1, -2, -2, 1, -2, 4, -2, -2, 1, 4, -2, -2, -2, 4, 4, 8, -2, -2, -2, -2, 4, 4, -2, 4, 1, 4, -2, -2, -2, -8, -2, -16, 4, 4, 4, 1, -2, 4, 4, 4, -2, -8, -2, -2, -2, 4, -2, -16, 1, -2, 4, -2, -2, 4, 4, 4, 4, 4, -2, 4, -2, 4, -2, 20, 4, -8, -2, -2, 4, -8, -2, -2, -2, 4, -2, -2, 4, -8, -2, -16, 8, 4, -2, 4, 4, 4, 4, 4

Offset: 1

Author

Antti Karttunen, Jun 09 2022

Keywords

• sign
• mult

Comments

Multiplicative because A293442 is.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537

Crossrefs

Cf. A019565, A293442.

Programs

PARI

A019565(n) = { my(m=1, p=1); while(n>0, p = nextprime(1+p); if(n%2, m *= p); n >>= 1); (m); };
A293442(n) = factorback(apply(e -> A019565(e),factor(n)[,2]));
memoA354825 = Map();
A354825(n) = if(1==n,1,my(v); if(mapisdefined(memoA354825,n,&v), v, v = -sumdiv(n,d,if(dA293442(n/d)*A354825(d),0)); mapput(memoA354825,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA293442(n/d) * a(d).