A244509 Order of GL_2(p), the general linear group over F_p, where p runs through the primes.

6, 48, 480, 2016, 13200, 26208, 78336, 123120, 267168, 682080, 892800, 1822176, 2755200, 3337488, 4773696, 7738848, 11908560, 13615200, 19845936, 25048800, 28003968, 38450880, 46879728, 62029440, 87607296, 103020000, 111447648, 129843216, 139851360

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Abbey Bourdon, Ozlem Ejder, Yuan Liu, Frances Odumodu, Bianca Viray, On the level of modular curves that give rise to sporadic j-invariants, arXiv:1808.04520 [math.NT], 2018. See Table 7.2 (an extract of current sequence).

Formula

a(n) = (p-1)*p*(p^2-1) where p = prime(n).

a(n) = A127917(n)*(prime(n)-1).

Subsequence of A047927. - Michel Marcus, Nov 25 2014

Example

For n=3 (p=5) we have a(3) = 4*5*(25-1) = 480.

Mathematica

gl2psz[p_] := (p - 1) p (p^2 - 1); sqg = gl2psz/@Prime@Range[m]
Table[(Prime[n] - 1) Prime[n] (Prime[n]^2 - 1), {n, 30}] (* Vincenzo Librandi, Aug 15 2018 *)

Prog

(PARI) a(n) = { my(p=prime(n)); (p-1)*p*(p^2-1) } \\ Joerg Arndt, Nov 23 2014
(Magma) [(NthPrime(n)-1)*NthPrime(n)*(NthPrime(n)^2-1): n in [1..100]]; // Vincenzo Librandi, Aug 15 2018

Crossrefs

Cf. A127917 (order of SL_2(p)), A047927.

Sequence in context: A319292 A261834 A226740 * A105627 A051578 A052639

Adjacent sequences: A244506 A244507 A244508 * A244510 A244511 A244512

Keyword

nonn

Author

John McGee, Nov 15 2014

Status

approved