A335000 Orders of the groups PSL(m,q) in increasing order as q runs through the prime powers (with repetitions).

6, 12, 60, 60, 168, 168, 360, 504, 660, 1092, 2448, 3420, 4080, 5616, 6072, 7800, 9828, 12180, 14880, 20160, 20160, 25308, 32736, 34440, 39732, 51888, 58800, 74412, 102660, 113460, 150348, 178920, 194472, 246480, 262080, 265680, 285852, 352440, 372000, 456288, 515100, 546312

Offset

1,1

Comments

60 is the order of PSL(2,4) and of PSL(2,5).

168 is the order of PSL(2,7) and of PSL(3,2).

20160 is the order of PSL(4,2) and of PSL(3,4).

Other repetitions > 20160 for PSL(m,q) groups are not known.

See A334884 and A334994 for variations of this sequence.

Links

Table of n, a(n) for n=1..42.

Wikipedia, Projective linear group.

Index entries for sequences related to groups.

Formula

#PSL(m,q) = (Product_{j=0..m-2} (q^m - q^j)) * q^(m-1) / gcd(m,q-1). - Bernard Schott, May 19 2020

Example

a(5) = #PSL(2,7) = (7^2-1)*7/gcd(2,6) = 168, and,
a(6) = #PSL(3,2) = (2^3-1)*(2^3-2)*2^2/gcd(3,1) = 168.

Crossrefs

Cf. A002884 \ {1} (PSL(n,2)), A117762 (PSL(2, prime(n))).

Cf. A334884 (another case with repetitions), A334994 (without repetitions).

Sequence in context: A337739 A076305 A088944 * A352806 A033931 A228847

Adjacent sequences: A334997 A334998 A334999 * A335001 A335002 A335003

Keyword

nonn

Author

Michel Marcus, May 19 2020

Status

approved