A175190 Number of irreducible factors in the factorization of the polynomial x^n + x + 1 over the integers mod 2.

0, 1, 1, 1, 2, 1, 1, 2, 1, 2, 2, 3, 2, 3, 1, 2, 3, 2, 4, 3, 2, 1, 3, 2, 3, 4, 2, 1, 2, 1, 3, 4, 3, 2, 2, 3, 2, 3, 3, 4, 3, 2, 2, 3, 4, 1, 3, 2, 3, 4, 4, 3, 4, 3, 3, 4, 3, 4, 6, 1, 2, 3, 1, 6, 5, 2, 2, 3, 4, 3, 5, 4, 5, 4, 4, 3, 4, 3, 5, 6, 3, 6, 4, 3, 4, 3, 5, 4, 5, 2, 2, 3, 4, 3, 3, 2, 3, 2, 2, 3, 6, 3, 5, 4, 3

Offset: 1

Author

Michel Lagneau, Mar 01 2010

Keywords

• nonn

Examples

			the factorization of x^5+x+1 over integers mod 2 is (1+x^2+x^3)(1+x+x^2), which has two unique factors
		

Crossrefs

Cf. A000374

Programs

Maple

with(numtheory): for k from 1 to 200 do:liste:=Factors(x^k+ x +1) mod 2; t1 := liste[2]:t2 := (liste[2][i], i=1..nops(t1)):print(nops(t1)) ;od :