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%I #36 Jan 29 2024 05:25:15
%S 6,12,60,168,660,1092,2448,3420,6072,12180,14880,25308,34440,39732,
%T 51888,74412,102660,113460,150348,178920,194472,246480,285852,352440,
%U 456288,515100,546312,612468,647460,721392,1024128,1123980,1285608,1342740,1653900
%N a(1) = 6; for n>1, a(n) = prime(n)*(prime(n)^2 - 1)/2.
%C a(n) is the order of the matrix group PSL(2,prime(n)). - corrected by _Tom Edgar_, Sep 28 2015
%D Blyth and Robertson, Essential Student Algebra, Volume 5: Groups,Chapman and Hall, New York, page 14
%H G. C. Greubel, <a href="/A117762/b117762.txt">Table of n, a(n) for n = 1..1000</a>
%F a(n) = A127918(n), n>1.
%F a(n) = A000040(n)*A084921(n). - _R. J. Mathar_, Jan 29 2024
%t a[n_]= If[n==1, 6, Prime[n]*(Prime[n]^2 -1)/2];
%t Table[a[n], {n,40}]
%t Join[{6}, Table[Prime[n] (Prime[n]^2 - 1)/2, {n, 2, 40}]] (* _Vincenzo Librandi_, Sep 29 2015 *)
%o (PARI) a(n) = prime(n)*(prime(n)^2-1)/2;
%o vector(40, n, a(n+1)) \\ _Altug Alkan_, Sep 28 2015
%o (Magma) [6] cat [NthPrime(n)*(NthPrime(n)^2-1)/2: n in [2..40]]; // _Vincenzo Librandi_, Sep 29 2015
%o (SageMath)
%o def A117762(n): return nth_prime(n)*(nth_prime(n)^2-1)/2 + 3*int(n==1)
%o [A117762(n) for n in range(1,41)] # _G. C. Greubel_, Jul 21 2023
%Y Cf. A084920, A127918.
%K nonn,easy
%O 1,1
%A _Roger L. Bagula_, Apr 14 2006
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