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

1,5

Links

Table of n, a(n) for n=1..105.

Example

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

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 :

Crossrefs

Cf. A000374

Sequence in context: A050205 A281530 A340260 * A317685 A257540 A333516

Adjacent sequences: A175187 A175188 A175189 * A175191 A175192 A175193

Keyword

nonn

Author

Michel Lagneau, Mar 01 2010

Status

approved