login

Reminder: The OEIS is hiring a new managing editor, and the application deadline is January 26.

Number of proper divisors of n that are irreducible when their binary expansion is interpreted as polynomial over GF(2).
5

%I #10 Nov 11 2017 12:04:54

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

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

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

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

%H Antti Karttunen, <a href="/A294881/b294881.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, d < n} A091225(d).

%F a(n) + A294882(n) = A032741(n).

%F a(n) = A294883(n) - A091225(n).

%o (PARI) A294881(n) = sumdiv(n,d,(d<n) * polisirreducible(Mod(1, 2) * Pol(binary(d))));

%Y Cf. A032741, A091225, A294882, A294883.

%Y Cf. also A234741, A234742, A294891.

%K nonn

%O 1,6

%A _Antti Karttunen_, Nov 09 2017