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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).
3
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
1,17
FORMULA
a(n) = A091222(n) - A001222(n).
For all n, a(A091206(n)) = 0. [Note that zeros occur in other positions as well.]
PROG
(PARI)
A091222(n) = vecsum(factor(Pol(binary(n))*Mod(1, 2))[, 2]);
A305802(n) = (A091222(n) - bigomega(n));
CROSSREFS
Cf. also A305789.
Sequence in context: A186717 A344833 A233286 * A375483 A186038 A091009
KEYWORD
sign
AUTHOR
Antti Karttunen, Jun 10 2018
STATUS
approved