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

1,12

Links

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

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A038548(n/d) * a(d).

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

Prog

(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(d<n, A038548(n/d)*A369453(d), 0)); mapput(memoA369453, n, v); (v)));

Crossrefs

Cf. A038548.

Cf. also A359763, A369454.

Sequence in context: A377334 A376971 A039964 * A340655 A035172 A387880

Adjacent sequences: A369450 A369451 A369452 * A369454 A369455 A369456

Keyword

sign

Author

Antti Karttunen, Jan 27 2024

Status

approved