A345463 Number of n X n matrices over GF(2) whose characteristic polynomial is irreducible.

2, 2, 48, 4032, 1935360, 2879815680, 23222833643520, 629183972848435200, 76669842195418919731200, 35461948770962722105432473600, 69793654310697320331920603401420800, 526981774867699711240400039137800880128000, 16622838761287803491875715175557341313583022080000

Offset: 1

Author

Geoffrey Critzer, Jun 20 2021

Keywords

• nonn

Crossrefs

Cf. A000225, A001037, A002884.

Programs

Mathematica

nn = 12; A001037 = Table[1/n Sum[MoebiusMu[n/d] 2^d, {d, Divisors[n]}], {n, 1,
    nn}] Table[Product[2^n - 2^i, {i, 0, n - 1}], {n, 1, nn}]/ Table[2^n - 1, {n, 1, nn}]

Formula

a(n) = A001037(n)*A002884(n)/A000225(n).