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A091222 Number of irreducible polynomials dividing n-th GF(2)[X]-polynomial, counted with multiplicity.

%I A091222 #17 Jun 08 2015 04:05:23
%S A091222 0,1,1,2,2,2,1,3,2,3,1,3,1,2,3,4,4,3,1,4,2,2,2,4,1,2,3,3,2,4,1,5,2,5,
%T A091222 2,4,1,2,3,5,1,3,2,3,4,3,1,5,2,2,5,3,2,4,1,4,3,3,1,5,1,2,3,6,4,3,1,6,
%U A091222 2,3,2,5,1,2,4,3,2,4,2,6,2,2,3,4,6,3,1,4,2,5,1,4,2,2,3,6,1,3,3,3,3,6
%N A091222 Number of irreducible polynomials dividing n-th GF(2)[X]-polynomial, counted with multiplicity.
%H A091222 Robert Israel, <a href="/A091222/b091222.txt">Table of n, a(n) for n = 1..10000</a>
%H A091222 A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>
%H A091222 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%F A091222 a(n) = A001222(A091203(n)) = A001222(A091205(n)).
%F A091222 a(A000051(n)) = A091248(n).
%p A091222 for n from 1 to 1000 do
%p A091222   L:= convert(n,base,2);
%p A091222   P:= add(L[i]*X^(i-1),i=1..nops(L));
%p A091222   R:= Factors(P) mod 2;
%p A091222   a[n]:= add(r[2],r=R[2]);
%p A091222 od:
%p A091222 seq(a[n],n=1..1000); # _Robert Israel_, Jun 07 2015
%o A091222 (PARI) a(n)=my(fm=factor(Pol(binary(n))*Mod(1, 2))); sum(k=1, #fm~, fm[k, 2]) \\ _Franklin T. Adams-Watters_, Jun 07 2015
%Y A091222 Cf. A000051, A001222, A091203, A091205, A091248.
%Y A091222 Cf. A256170.
%K A091222 nonn
%O A091222 1,4
%A A091222 _Antti Karttunen_, Jan 03 2004