A277013 a(n) = number of irreducible polynomial factors (counted with multiplicity) in the n-th Stern polynomial B(n,t).

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

Offset: 1

Author

Antti Karttunen, Oct 07 2016

Keywords

• nonn

Examples

			B(11,t) = t^2 + 3t + 1 which is irreducible, so a(11) = 1.
B(12,t) = t^3 + t^2 = t^2(t+1), so a(12) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..85085

Crossrefs

Cf. A186891 (positions of 0 and 1's in this sequence), A277027 (terms squared).

Cf. A000079, A125184, A277322, A260443.

Differs from A001222 for the first time at n=25, where a(25)=1. A277190 gives the positions of differing terms.

Programs

PARI

A277013 = n -> vecsum(factor(ps(n))[,2]);
ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2))); \\ From Charles R Greathouse IV code in A186891.
for(n=1, 85085, write("b277013.txt", n, " ", A277013(n)));

Formula

a(n) = A277322(A260443(n)).

It seems that for all n >= 1, a(2^n) = n.