A294883 - OEIS

%I #8 Nov 11 2017 12:05:15

%S 0,1,1,1,0,2,1,1,1,1,1,2,1,2,1,1,0,2,1,1,2,2,0,2,1,2,1,2,0,2,1,1,2,1,

%T 1,2,1,2,2,1,1,3,0,2,1,1,1,2,1,2,1,2,0,2,2,2,2,1,1,2,1,2,2,1,1,3,1,1,

%U 1,2,0,2,1,2,2,2,2,3,0,1,1,2,0,3,0,1,2,2,0,2,3,1,2,2,1,2,1,2,2,2,0,2,1,2,2

%N Number of divisors of n that are irreducible when their binary expansion is interpreted as polynomial over GF(2).

%C Number of terms of A014580 that divide n.

%H Antti Karttunen, <a href="/A294883/b294883.txt">Table of n, a(n) for n = 1..21845</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences related to polynomials in ring GF(2)[X]</a>

%F a(n) = Sum_{d|n} A091225(d).

%F a(n) + A294884(n) = A000005(n).

%F a(n) = A294881(n) + A091225(n).

%o (PARI) A294883(n) = sumdiv(n,d,polisirreducible(Mod(1, 2)*Pol(binary(d))));

%Y Cf. A000005, A014580, A091225, A294881, A294884.

%Y Cf. A091209 (gives a subset of zeros).

%Y Cf. also A234741, A234742, A294893.

%K nonn

%O 1,6

%A _Antti Karttunen_, Nov 09 2017