A305822 Number of irreducible factors (counted with multiplicity) of the (0,1)-polynomial encoded in the binary expansion of n has when it is factored over Q.

0, 1, 1, 2, 1, 2, 1, 3, 2, 2, 1, 3, 1, 2, 2, 4, 1, 3, 1, 3, 2, 2, 1, 4, 1, 2, 3, 3, 1, 3, 1, 5, 2, 2, 2, 4, 1, 2, 2, 4, 1, 3, 1, 3, 3, 2, 1, 5, 2, 2, 2, 3, 1, 4, 1, 4, 2, 2, 1, 4, 1, 2, 3, 6, 2, 3, 1, 3, 1, 3, 1, 5, 1, 2, 3, 3, 1, 3, 1, 5, 1, 2, 1, 4, 2, 2, 1, 4, 1, 4, 1, 3, 2, 2, 2, 6, 1, 3, 3, 3, 1, 3, 1, 4, 3

Offset

1,4

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

For all n >= 1, a(n) >= A206719(n).

Prog

(PARI) A305822(n) = vecsum(factor(Pol(binary(n)))[, 2]);

Crossrefs

Cf. A206074 (gives the positions of 1's), A206719, A257000, A304751.

Cf. also A001222, A091222.

Differs from A277013 for the first time at n=65, where a(65) = 2, while A277013(65) = 1.

Sequence in context: A122810 A179953 A277013 * A326190 A086436 A001222

Adjacent sequences: A305819 A305820 A305821 * A305823 A305824 A305825

Keyword

nonn

Author

Antti Karttunen, Jun 10 2018

Status

approved