A378437 Dirichlet inverse of A033630, where A033630 is the number of partitions of n into distinct divisors of n.

1, -1, -1, 0, -1, 0, -1, 0, 0, 1, -1, 0, -1, 1, 1, 0, -1, 0, -1, -1, 1, 1, -1, -2, 0, 1, 0, -1, -1, -2, -1, 0, 1, 1, 1, -2, -1, 1, 1, -1, -1, -1, -1, 0, 0, 1, -1, -2, 0, 0, 1, 0, -1, 0, 1, 0, 1, 1, -1, -26, -1, 1, 0, 0, 1, -1, -1, 0, 1, -1, -1, -14, -1, 1, 0, 0, 1, 0, -1, -1, 0, 1, -1, -19, 1, 1, 1, -1, -1, -17, 1, 0, 1, 1, 1

Offset: 1

Author

Antti Karttunen, Nov 26 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A033630, A378438 (Möbius transform).

Programs

PARI

A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
memoA378437 = Map();
A378437(n) = if(1==n,1,my(v); if(mapisdefined(memoA378437,n,&v), v, v = -sumdiv(n,d,if(dA033630(n/d)*A378437(d),0)); mapput(memoA378437,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA033630(n/d) * a(d).