cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A335804 Number of n X n matrices over GF(2) with minimal polynomial x^n - 1.

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%I A335804 #14 Jul 24 2025 08:37:48
%S A335804 1,3,56,2520,666624,839946240,3343877406720,41781748196966400,
%T A335804 3701652434038082764800,763416952708225267547504640,
%U A335804 750836199529096452135514747699200
%N A335804 Number of n X n matrices over GF(2) with minimal polynomial x^n - 1.
%C A335804 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).
%C A335804 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
%F A335804 a(n) = A002884(n) / A003473(n). If n is an odd prime, then a(n) = A089035(n).
%Y A335804 Cf. A002884, A003473, A027362, A089035.
%K A335804 nonn
%O A335804 1,2
%A A335804 _Christof Beierle_, Jun 24 2020