A175190 - OEIS

%I #2 Mar 30 2012 18:35:52

%S 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,

%T 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,

%U 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

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

%e 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

%p 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 :

%Y Cf. A000374

%K nonn

%O 1,5

%A _Michel Lagneau_, Mar 01 2010