A334994 Orders of the groups PSL(m,q) in increasing order as q runs through the prime powers (without repetitions).

6, 12, 60, 168, 360, 504, 660, 1092, 2448, 3420, 4080, 5616, 6072, 7800, 9828, 12180, 14880, 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) or PSL(2,5).

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

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

See A334884 and A335000 for variations of this sequence.

Links

Table of n, a(n) for n=1..39.

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

#PSL(2,7) = (7^2-1)*7/gcd(2,6) = 168 = a(4), and,
#PSL(3,2) = (2^3-1)*(2^3-2)*2^2/gcd(3,1) = 168 = a(4).

Crossrefs

Cf. A117762 (PSL(2, prime(n))).

Cf. A334884 and A335000 (both with repetitions, but different).

Sequence in context: A228847 A093901 A334884 * A117762 A178957 A104362

Adjacent sequences: A334991 A334992 A334993 * A334995 A334996 A334997

Keyword

nonn

Author

Michel Marcus, May 19 2020

Status

approved