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Number of irreducible polynomials dividing n-th GF(2)[X]-polynomial, counted with multiplicity.
22

%I #17 Jun 08 2015 04:05:23

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

%H Robert Israel, <a href="/A091222/b091222.txt">Table of n, a(n) for n = 1..10000</a>

%H A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>

%F a(n) = A001222(A091203(n)) = A001222(A091205(n)).

%F a(A000051(n)) = A091248(n).

%p for n from 1 to 1000 do

%p L:= convert(n,base,2);

%p P:= add(L[i]*X^(i-1),i=1..nops(L));

%p R:= Factors(P) mod 2;

%p a[n]:= add(r[2],r=R[2]);

%p od:

%p seq(a[n],n=1..1000); # _Robert Israel_, Jun 07 2015

%o (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 Cf. A000051, A001222, A091203, A091205, A091248.

%Y Cf. A256170.

%K nonn

%O 1,4

%A _Antti Karttunen_, Jan 03 2004