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A294892 Number of proper divisors d of n such that either d=1 or Stern polynomial B(d,x) is reducible.

%I A294892 #9 Nov 11 2017 12:05:41
%S A294892 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 A294892 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 A294892 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 A294892 Number of proper divisors d of n such that either d=1 or Stern polynomial B(d,x) is reducible.
%H A294892 Antti Karttunen, <a href="/A294892/b294892.txt">Table of n, a(n) for n = 1..22001</a>
%F A294892 a(n) = Sum_{d|n, d<n} (1-A283991(d)).
%F A294892 a(n) + A294891(n) = A032741(n).
%F A294892 a(n) = A294894(n) + A283991(n) - 1.
%e A294892 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 A294892 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 A294892 (PARI)
%o A294892 ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));
%o A294892 A283991(n) = polisirreducible(ps(n));
%o A294892 A294892(n) = sumdiv(n,d,(d<n)*(0==A283991(d)));
%Y A294892 Cf. A186891, A283991, A294891, A294893, A294894.
%Y A294892 Cf. also A294882, A294902.
%K A294892 nonn
%O A294892 1,8
%A A294892 _Antti Karttunen_, Nov 10 2017