A378451 Dirichlet inverse of A119347, where A119347(n) is the number of distinct sums of distinct divisors of n.

1, -3, -3, 2, -3, 6, -3, 0, 2, 3, -3, 5, -3, 3, 3, 0, -3, -6, -3, 9, 3, 3, -3, -12, 2, 3, 0, -5, -3, 18, -3, 0, 3, 3, 3, 13, -3, 3, 3, 3, -3, -6, -3, -12, -4, 3, -3, 4, 2, -12, 3, -12, -3, -6, 3, 57, 3, 3, -3, -15, -3, 3, -8, 0, 3, -54, -3, -12, 3, -34, -3, -39, -3, 3, -12, -12, 3, -78, -3, -24, 0, 3, -3, 157, 3, 3, 3

Offset: 1

Author

Antti Karttunen, Nov 29 2024

Keywords

• sign

Links

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

Crossrefs

Cf. A119347.

Programs

PARI

A119347(n) = { my(c=[0]); fordiv(n,d, c = Set(concat(c,vector(#c,i,c[i]+d)))); (#c)-1; };
memoA378451 = Map();
A378451(n) = if(1==n,1,my(v); if(mapisdefined(memoA378451,n,&v), v, v = -sumdiv(n,d,if(dA119347(n/d)*A378451(d),0)); mapput(memoA378451,n,v); (v)));

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA119347(n/d) * a(d).