OFFSET
0,2
COMMENTS
Equivalently, number of n X n matrices over GF(2) that are diagonalizable over the algebraic closure of GF(2).
Equivalently, the number of n X n matrices over GF(2) whose minimal polynomial is a product of distinct irreducible factors, i.e., the minimal polynomial is squarefree.
LINKS
Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.
FORMULA
MATHEMATICA
nn = 13; q = 2; A001037 =Table[1/n Sum[MoebiusMu[n/d] q^d, {d, Divisors[n]}], {n, 1, nn}]; \[Gamma]q[j_, d_] :=Table[Product[(q^d)^n - (q^d)^i, {i, 0, n - 1}], {n, 1, nn}][[j]]; Table[Product[q^n - q^i, {i, 0, n - 1}], {n, 0, nn}] CoefficientList[ Series[Product[(1 + Sum[u^(j d)/\[Gamma]q[j, d], {j, 1, nn}])^
A001037[[d]], {d, 1, nn}], {u, 0, nn}], u]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Jul 11 2021
STATUS
approved