A378440 Dirichlet inverse of Möbius transform of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

1, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -3, 0, 0, 0, -1, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, -5, 0, 0, 0, 0, 0, -1, 0, -1, 0, 0, 0, -29, 0, 0, 0, 0, 0, -1, 0, 0, 0, 0, 0, -19, 0, 0, 0, 0, 0, 0, 0, -3, 0, 0, 0, -21, 0, 0, 0, -1, 0, -19, 0, 0, 0, 0, 0, -11, 0, 0, 0, -1

Offset: 1

Author

Antti Karttunen, Nov 27 2024

Keywords

• sign

Comments

Equally, inverse Möbius transform of A378437, which is the Dirichlet inverse of A033630.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000

Crossrefs

Inverse Möbius transform of A378437.

Dirichlet inverse of A378439.

Cf. A033630.

Programs

PARI

A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
A378439(n) = sumdiv(n, d, moebius(n/d)*A033630(d));
memoA378440 = Map();
A378440(n) = if(1==n,1,my(v); if(mapisdefined(memoA378440,n,&v), v, v = -sumdiv(n,d,if(dA378439(n/d)*A378440(d),0)); mapput(memoA378440,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378439(n/d) * a(d).

a(n) = Sum_{d|n} A378437(d).