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

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 03 2004

Keywords

• nonn

Links

• Robert Israel, Table of n, a(n) for n = 1..10000
• A. Karttunen, Scheme-program for computing this sequence.
• Index entries for sequences operating on GF(2)[X]-polynomials

Crossrefs

Cf. A000051, A001222, A091203, A091205, A091248.

Cf. A256170.

Programs

Maple

for n from 1 to 1000 do
  L:= convert(n,base,2);
  P:= add(L[i]*X^(i-1),i=1..nops(L));
  R:= Factors(P) mod 2;
  a[n]:= add(r[2],r=R[2]);
od:
seq(a[n],n=1..1000); # Robert Israel, Jun 07 2015

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

Formula

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

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