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
Keywords
Examples
For n=3 (p=5) we have a(3) = 4*5*(25-1) = 480.
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).
Programs
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Magma
[(NthPrime(n)-1)*NthPrime(n)*(NthPrime(n)^2-1): n in [1..100]]; // Vincenzo Librandi, Aug 15 2018
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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 *) -
PARI
a(n) = { my(p=prime(n)); (p-1)*p*(p^2-1) } \\ Joerg Arndt, Nov 23 2014
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
Sum 1/a(n) = A382584. - R. J. Mathar, Mar 31 2025