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

%I A244509 #33 Mar 31 2025 14:42:58
%S A244509 6,48,480,2016,13200,26208,78336,123120,267168,682080,892800,1822176,
%T A244509 2755200,3337488,4773696,7738848,11908560,13615200,19845936,25048800,
%U A244509 28003968,38450880,46879728,62029440,87607296,103020000,111447648,129843216,139851360
%N A244509 Order of GL_2(p), the general linear group over F_p, where p runs through the primes.
%H A244509 Vincenzo Librandi, <a href="/A244509/b244509.txt">Table of n, a(n) for n = 1..1000</a>
%H A244509 Abbey Bourdon, Ozlem Ejder, Yuan Liu, Frances Odumodu, Bianca Viray, <a href="https://arxiv.org/abs/1808.04520">On the level of modular curves that give rise to sporadic j-invariants</a>, arXiv:1808.04520 [math.NT], 2018. See Table 7.2 (an extract of current sequence).
%F A244509 a(n) = (p-1)*p*(p^2-1) where p = prime(n).
%F A244509 a(n) = A127917(n)*(prime(n)-1).
%F A244509 Subsequence of A047927. - _Michel Marcus_, Nov 25 2014
%F A244509 Sum 1/a(n) = A382584. - _R. J. Mathar_, Mar 31 2025
%e A244509 For n=3 (p=5) we have a(3) = 4*5*(25-1) = 480.
%t A244509 gl2psz[p_] := (p - 1) p (p^2 - 1); sqg = gl2psz/@Prime@Range[m]
%t A244509 Table[(Prime[n] - 1) Prime[n] (Prime[n]^2 - 1), {n, 30}] (* _Vincenzo Librandi_, Aug 15 2018 *)
%o A244509 (PARI) a(n) = { my(p=prime(n)); (p-1)*p*(p^2-1) } \\ _Joerg Arndt_, Nov 23 2014
%o A244509 (Magma) [(NthPrime(n)-1)*NthPrime(n)*(NthPrime(n)^2-1): n in [1..100]]; // _Vincenzo Librandi_, Aug 15 2018
%Y A244509 Cf. A127917 (order of SL_2(p)), A047927.
%K A244509 nonn
%O A244509 1,1
%A A244509 _John McGee_, Nov 15 2014