A369453 Dirichlet inverse of A038548, where A038548 is the number of divisors of n that are at most sqrt(n).

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

Offset: 1

Author

Antti Karttunen, Jan 27 2024

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537

Crossrefs

Cf. A038548.

Cf. also A359763, A369454.

Programs

PARI

A038548(n) = if( n<1, 0, sumdiv(n, d, d*d <= n))
memoA369453 = Map();
A369453(n) = if(1==n,1,my(v); if(mapisdefined(memoA369453,n,&v), v, v = -sumdiv(n,d,if(dA038548(n/d)*A369453(d),0)); mapput(memoA369453,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA038548(n/d) * a(d).

Dirichlet g.f.: 2/(zeta(s)^2 + zeta(2*s)).