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

1,4

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

Formula

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

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

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

Prog

(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

Crossrefs

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

Cf. A256170.

Sequence in context: A037180 A241675 A349273 * A316506 A294884 A275024

Adjacent sequences: A091219 A091220 A091221 * A091223 A091224 A091225

Keyword

nonn

Author

Antti Karttunen, Jan 03 2004

Status

approved