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

Author

Antti Karttunen, Jun 10 2018

Keywords

• nonn

Links

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

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.

Programs

PARI

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

Formula

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