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

1,4

Links

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

Formula

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

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

Example

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.

Prog

(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)));

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.

Sequence in context: A318322 A122810 A179953 * A305822 A326190 A086436

Adjacent sequences: A277010 A277011 A277012 * A277014 A277015 A277016

Keyword

nonn

Author

Antti Karttunen, Oct 07 2016

Status

approved