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A294884 Number of divisors of n that are not irreducible when their binary expansion is interpreted as polynomial over GF(2).

%I A294884 #10 Nov 11 2017 12:05:23
%S A294884 1,1,1,2,2,2,1,3,2,3,1,4,1,2,3,4,2,4,1,5,2,2,2,6,2,2,3,4,2,6,1,5,2,3,
%T A294884 3,7,1,2,2,7,1,5,2,4,5,3,1,8,2,4,3,4,2,6,2,6,2,3,1,10,1,2,4,6,3,5,1,5,
%U A294884 3,6,2,10,1,2,4,4,2,5,2,9,4,2,2,9,4,3,2,6,2,10,1,5,2,2,3,10,1,4,4,7,2,6,1,6,6
%N A294884 Number of divisors of n that are not irreducible when their binary expansion is interpreted as polynomial over GF(2).
%C A294884 One more than the number of terms of A091242 that divide n: +1 is for divisor 1, which is also included in the count.
%H A294884 Antti Karttunen, <a href="/A294884/b294884.txt">Table of n, a(n) for n = 1..21845</a>
%H A294884 <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>
%F A294884 a(n) = Sum_{d|n} (1-A091225(d)).
%F A294884 a(n) + A294883(n) = A000005(n).
%F A294884 For n > 1, a(n) = 1 + A294882(n) - A091225(n).
%o A294884 (PARI) A294884(n) = sumdiv(n,d,!polisirreducible(Mod(1, 2)*Pol(binary(d))));
%Y A294884 Cf. A000005, A091225, A091242, A294882, A294883.
%Y A294884 Cf. also A234741, A234742, A294894.
%K A294884 nonn
%O A294884 1,4
%A A294884 _Antti Karttunen_, Nov 09 2017