A378438 Dirichlet inverse of A378436, where A378436 is the inverse Möbius transform of the number of partitions of n into distinct divisors of n.

1, -2, -2, 1, -2, 3, -2, 0, 1, 4, -2, -1, -2, 4, 4, 0, -2, -1, -2, -3, 4, 4, -2, -2, 1, 4, 0, -3, -2, -8, -2, 0, 4, 4, 4, -2, -2, 4, 4, 0, -2, -7, -2, -2, -2, 4, -2, 0, 1, -2, 4, -2, -2, 0, 4, 1, 4, 4, -2, -21, -2, 4, -2, 0, 4, -7, -2, -2, 4, -8, -2, -10, -2, 4, -2, -2, 4, -6, -2, 0, 0, 4, -2, -15, 4, 4, 4, -1, -2

Offset: 1

Author

Antti Karttunen, Nov 26 2024

Keywords

• sign

Comments

Equivalently, Möbius transform of the Dirichlet inverse of A033630.

Links

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

Crossrefs

Cf. A008683, A033630.

Dirichlet inverse of A378436.

Möbius transform of A378437.

Programs

PARI

A033630(n) = if(!n, 1, my(p=1); fordiv(n, d, p *= (1 + 'x^d)); polcoeff(p, n));
A378436(n) = sumdiv(n,d,A033630(d));
memoA378438 = Map();
A378438(n) = if(1==n,1,my(v); if(mapisdefined(memoA378438,n,&v), v, v = -sumdiv(n,d,if(dA378436(n/d)*A378438(d),0)); mapput(memoA378438,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA378436(n/d) * a(d).

a(n) = Sum_{d|n} A008683(n/d)*A378437(d).