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

1,36

Links

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

Formula

a(1) = 1, and for n > 1, a(n) = -Sum_{d|n, d<n} A322353(n/d) * a(d).

Prog

(PARI)
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(d<n, A322353(n/d)*A359786(d), 0)); mapput(memoA359786, n, v); (v)));

Crossrefs

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

Sequence in context: A348452 A309163 A320655 * A359763 A277017 A178498

Adjacent sequences: A359783 A359784 A359785 * A359787 A359788 A359789

Keyword

sign

Author

Antti Karttunen, Jan 16 2023

Status

approved