login
A277013
a(n) = number of irreducible polynomial factors (counted with multiplicity) in the n-th Stern polynomial B(n,t).
17
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
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).
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
KEYWORD
nonn
AUTHOR
Antti Karttunen, Oct 07 2016
STATUS
approved