1,2

a(n) is the size of the conjugacy class in GL(n,GF(2)) corresponding to the companion matrix of x^n - 1. It can be given by the number of n X n invertible matrices over GF(2) divided by the number of n X n circulant invertible matrices over GF(2) (i.e., the centralizer of the companion matrix of x^n - 1).

If m is odd, x^m-1 has no multiple roots so that every matrix with characteristic polynomial x^m-1 also has x^m-1 as its minimal polynomial. Hence, a(m) = A089035(m). - Geoffrey Critzer, Jul 24 2025

a(n) = A002884(n) / A003473(n). If n is an odd prime, then a(n) = A089035(n).

Cf. A002884, A003473, A027362, A089035.

Sequence in context: A241136 A202029 A287396 * A070731 A385832 A132489

Adjacent sequences: A335801 A335802 A335803 * A335805 A335806 A335807

Christof Beierle, Jun 24 2020

approved