A305802 Difference in number of prime factors (when counted with multiplicity) between GF(2)[X] (carryless binary) and ordinary factorization: a(n) = A091222(n) - A001222(n).

0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 3, 0, 0, 1, 0, 0, 1, 0, -1, 0, 0, 0, 1, 1, 0, 0, 0, 3, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 1, 1, 0, 0, 0, -1, 3, 0, 1, 0, -1, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 0, 0, 3, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, -2, 0, 2, 0, 4, 1, -1, 0, 1, 1, -1, 1, 0, 0, 1, 0, 0, 0, 0, -1, 2, 3, 0, 0, 1

Offset: 1

Author

Antti Karttunen, Jun 10 2018

Keywords

• sign

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences operating on polynomials in ring GF(2)[X]

Crossrefs

Cf. A001222, A091222, A091206, A305816.

Cf. also A305789.

Programs

PARI

A091222(n) = vecsum(factor(Pol(binary(n))*Mod(1, 2))[, 2]);
A305802(n) = (A091222(n) - bigomega(n));

Formula

a(n) = A091222(n) - A001222(n).

For all n, a(A091206(n)) = 0. [Note that zeros occur in other positions as well.]