A060615 Number of conjugacy classes in the group GL_2(K) when K is a finite field with q = p^m for a prime p and m >= 1.

3, 8, 15, 24, 48, 63, 80, 120, 168, 255, 288, 360, 528, 624, 728, 840, 960, 1023, 1368, 1680, 1848, 2208, 2400, 2808, 3480, 3720, 4095, 4488, 5040, 5328, 6240, 6560, 6888, 7920, 9408, 10200, 10608, 11448, 11880, 12768, 14640, 15624, 16128, 16383, 17160

Offset: 0

Author

Ahmed Fares (ahmedfares(AT)my-deja.com), Apr 13 2001

Keywords

• nonn

Comments

The number of conjugacy classes in the group GL_2(K) is q^2 - 1 so this sequence is a subsequence of A005563 restricted to q = prime power. The order of the group GL_2(K) is in A059238.

Crossrefs

A000961, A005563, A059238. A diagonal of A060638.

Programs

Maple

with(numtheory): for n from 2 to 400 do if nops(ifactors(n)[2]) = 1 then printf(`%d,`, n^2-1) fi: od:

Formula

a(n) = A000961(n+2)^2 - 1. - Sean A. Irvine, Dec 04 2022

Extensions

More terms from James Sellers, Apr 14 2001