

A277013


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


16



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
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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: A116479 A122810 A179953 * A086436 A001222 A257091
Adjacent sequences: A277010 A277011 A277012 * A277014 A277015 A277016


KEYWORD

nonn


AUTHOR

Antti Karttunen, Oct 07 2016


STATUS

approved



