A359785 Dirichlet inverse of A320655, where A320655(n) is the number of factorizations of n into semiprimes.

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

Offset

1,60

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} A320655(n/d) * a(d).

Prog

(PARI)
A320655(n, m=n) = if(1==n, 1, my(s=0); fordiv(n, d, if((2==bigomega(d)&&(d<=m)), s += A320655(n/d, d))); (s));
memoA359785 = Map();
A359785(n) = if(1==n, 1, my(v); if(mapisdefined(memoA359785, n, &v), v, v = -sumdiv(n, d, if(d<n, A320655(n/d)*A359785(d), 0)); mapput(memoA359785, n, v); (v)));

Crossrefs

Cf. A320655, A322353 (seems to give the absolute values), A359786.

Sequence in context: A332042 A171368 A322353 * A378214 A133988 A089812

Adjacent sequences: A359782 A359783 A359784 * A359786 A359787 A359788

Keyword

sign

Author

Antti Karttunen, Jan 16 2023

Status

approved