%I #13 Jul 02 2018 07:03:14
%S 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,
%T 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,
%U 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
%N 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).
%H Antti Karttunen, <a href="/A305802/b305802.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on polynomials in ring GF(2)[X]</a>
%F a(n) = A091222(n) - A001222(n).
%F For all n, a(A091206(n)) = 0. [Note that zeros occur in other positions as well.]
%o (PARI)
%o A091222(n) = vecsum(factor(Pol(binary(n))*Mod(1, 2))[, 2]);
%o A305802(n) = (A091222(n) - bigomega(n));
%Y Cf. A001222, A091222, A091206, A305816.
%Y Cf. also A305789.
%K sign
%O 1,17
%A _Antti Karttunen_, Jun 10 2018