%I #9 Nov 11 2017 12:05:41

%S 0,1,1,1,1,1,1,2,1,1,1,3,1,1,1,3,1,3,1,3,1,1,1,5,1,1,2,3,1,4,1,4,1,1,

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

%U 1,4,1,9,1,1,2,3,1,4,1,7,3,1,1,8,1,1,1,5,1,8,1,3,1,1,1,9,1,3,3,5,1,4,1,5,4

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

%H Antti Karttunen, <a href="/A294892/b294892.txt">Table of n, a(n) for n = 1..22001</a>

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

%F a(n) + A294891(n) = A032741(n).

%F a(n) = A294894(n) + A283991(n) - 1.

%e For n=48, its proper divisors are [1, 2, 3, 4, 6, 8, 12, 16, 24]. After 1, the divisors 4, 6, 8, 12, 16 and 24 are not found in A186891, thus a(48) = 1+6 = 7.

%e For n=50, its proper divisors are [1, 2, 5, 10, 25]. After 1, only 10 is not found in A186891, thus a(50) = 1+1 = 2.

%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 A294892(n) = sumdiv(n,d,(d<n)*(0==A283991(d)));

%Y Cf. A186891, A283991, A294891, A294893, A294894.

%Y Cf. also A294882, A294902.

%K nonn

%O 1,8

%A _Antti Karttunen_, Nov 10 2017