0,4

Number of primitive irreducible factors of x^(2n+1) - 1 over integers mod 2. There are no primitive irreducible factors for x^(2n)-1 because it always has the same factors as x^n-1. Considering that A000374 also counts the cycles in the map f(x) = 2x mod n, a(n) is also the number of primitive cycles of that mapping. - T. D. Noe (noe(AT)sspectra.com), Aug 01 2003

Equals number of irreducible factors of the cyclotomic polynomial Phi(2n+1,x) over Z/2Z. All factors have the same degree. - T. D. Noe, Mar 01 2008

T. D. Noe, Table of n, a(n) for n=0..10000

a(n) = Sum{d|2n+1} mu((2n+1)/d) A000374(d), the inverse Mobius transform of A000374 - T. D. Noe (noe(AT)sspectra.com), Aug 01 2003

A037225[ n ]/A002326[ n ].

Cf. A000374 (number of irreducible factors of x^n - 1 over integers mod 2), A081844.

Sequence in context: A043277 A025864 A070242 this_sequence A089641 A086995 A135230

Adjacent sequences: A037223 A037224 A037225 this_sequence A037227 A037228 A037229

nonn

N. J. A. Sloane (njas(AT)research.att.com).