A359785 -id:A359785 - cp's OEIS frontend

A359786 Dirichlet inverse of A322353, where A322353(n) is the number of factorizations of n into distinct semiprimes.

1, 0, 0, -1, 0, -1, 0, 0, -1, -1, 0, 0, 0, -1, -1, 1, 0, 0, 0, 0, -1, -1, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, -1, -1, 2, 0, -1, -1, 1, 0, 0, 0, 0, 0, -1, 0, 0, -1, 0, -1, 0, 0, 1, -1, 1, -1, -1, 0, 2, 0, -1, 0, -1, -1, 0, 0, 0, -1, 0, 0, 0, 0, -1, 0, 0, -1, 0, 0, 0, 1, -1, 0, 2, -1, -1, -1, 1, 0, 2, -1, 0, -1, -1, -1, -1, 0, 0, 0, 2, 0, 0, 0, 1, 0

Offset: 1

Graph
List
Refs
Listen
History
Text
Internal format

Antti Karttunen, Jan 16 2023

sign

Antti Karttunen, Table of n, a(n) for n = 1..100000

Cf. A320655 (seems to give the absolute values), A322353, A359785.

A322353(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((2==bigomega(d)&&(d<=m)), s += A322353(n/d, d-1))); (s));
memoA359786 = Map();
A359786(n) = if(1==n,1,my(v); if(mapisdefined(memoA359786,n,&v), v, v = -sumdiv(n,d,if(dA322353(n/d)*A359786(d),0)); mapput(memoA359786,n,v); (v)));

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, dA322353(n/d) * a(d).

cp's OEIS Frontend

A359786 Dirichlet inverse of A322353, where A322353(n) is the number of factorizations of n into distinct semiprimes.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Formula