%I #8 Nov 11 2017 12:05:56

%S 1,1,1,2,1,2,1,3,2,2,1,4,1,2,2,4,1,4,1,4,2,2,1,6,1,2,3,4,1,5,1,5,2,2,

%T 2,7,1,2,2,6,1,5,1,4,4,2,1,8,2,3,2,4,1,6,1,6,2,2,1,9,1,2,4,6,1,5,1,4,

%U 2,5,1,10,1,2,3,4,1,5,1,8,4,2,1,9,2,2,2,6,1,9,1,4,2,2,1,10,1,4,4,6,1,5,1,6,5

%N Number of divisors d of n such that either d=1 or Stern polynomial B(d,x) is reducible.

%H Antti Karttunen, <a href="/A294894/b294894.txt">Table of n, a(n) for n = 1..22001</a>

%F a(n) = Sum_{d|n} (1-A283991(d)).

%F a(n) + A294893(n) = A000005(n).

%F a(n) = 1 + A294892(n) - A283991(n).

%e For n=25, with divisors [1, 5, 25], both B(5,x) and B(25,x) are irreducible, so only 1 is counted and a(25)=1.

%o (PARI)

%o ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));

%o A283991(n) = polisirreducible(ps(n));

%o A294894(n) = sumdiv(n,d,(0==A283991(d)));

%Y Cf. A186891, A283991, A294891, A294892, A294893.

%Y Cf. also A294884, A294904.

%Y Differs from A033273 for the first time at n=25.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 10 2017