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A294891 Number of proper divisors d of n such that Stern polynomial B(d,x) is irreducible.

%I A294891 #8 Nov 11 2017 12:05:33
%S A294891 0,0,0,1,0,2,0,1,1,2,0,2,0,2,2,1,0,2,0,2,2,2,0,2,1,2,1,2,0,3,0,1,2,2,
%T A294891 2,2,0,2,2,2,0,3,0,2,2,2,0,2,1,3,2,2,0,2,2,2,2,2,0,3,0,2,2,1,2,3,0,2,
%U A294891 2,3,0,2,0,2,3,2,2,3,0,2,1,2,0,3,2,2,2,2,0,3,2,2,2,2,2,2,0,2,2,3,0,3,0,2,3
%N A294891 Number of proper divisors d of n such that Stern polynomial B(d,x) is irreducible.
%H A294891 Antti Karttunen, <a href="/A294891/b294891.txt">Table of n, a(n) for n = 1..22001</a>
%F A294891 a(n) = Sum_{d|n, d<n} A283991(d).
%F A294891 a(n) + A294892(n) = A032741(n).
%F A294891 a(n) = A294893(n) - A283991(n).
%e A294891 For n=50, with proper divisors [1, 2, 5, 10, 25], 2, 5, and 25 are larger than one and included in A186891, thus a(50) = 3.
%o A294891 (PARI)
%o A294891 ps(n) = if(n<2, n, if(n%2, ps(n\2)+ps(n\2+1), 'x*ps(n\2)));
%o A294891 A283991(n) = polisirreducible(ps(n));
%o A294891 A294891(n) = sumdiv(n,d,(d<n)*A283991(d));
%Y A294891 Cf. A186891, A283991, A294892, A294893, A294894.
%Y A294891 Cf. also A294881, A294901.
%Y A294891 Differs from A087624 for the first time at n=50.
%K A294891 nonn
%O A294891 1,6
%A A294891 _Antti Karttunen_, Nov 10 2017