%I #17 Oct 09 2016 19:42:36

%S 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,

%T 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,

%U 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

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

%H Antti Karttunen, <a href="/A277013/b277013.txt">Table of n, a(n) for n = 1..85085</a>

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

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

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

%e B(12,t) = t^3 + t^2 = t^2(t+1), so a(12) = 3.

%o (PARI)

%o A277013 = n -> vecsum(factor(ps(n))[,2]);

%o 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.

%o for(n=1, 85085, write("b277013.txt", n, " ", A277013(n)));

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

%Y Cf. A000079, A125184, A277322, A260443.

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

%K nonn

%O 1,4

%A _Antti Karttunen_, Oct 07 2016