A117762 a(1) = 6; for n>1, a(n) = prime(n)*(prime(n)^2 - 1)/2.

6, 12, 60, 168, 660, 1092, 2448, 3420, 6072, 12180, 14880, 25308, 34440, 39732, 51888, 74412, 102660, 113460, 150348, 178920, 194472, 246480, 285852, 352440, 456288, 515100, 546312, 612468, 647460, 721392, 1024128, 1123980, 1285608, 1342740, 1653900

Offset: 1

Author

Roger L. Bagula, Apr 14 2006

Keywords

• nonn
• easy

Comments

a(n) is the order of the matrix group PSL(2,prime(n)). - corrected by Tom Edgar, Sep 28 2015

References

• Blyth and Robertson, Essential Student Algebra, Volume 5: Groups,Chapman and Hall, New York, page 14

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A084920, A127918.

Programs

Magma

[6] cat [NthPrime(n)*(NthPrime(n)^2-1)/2: n in [2..40]]; // Vincenzo Librandi, Sep 29 2015

Mathematica

a[n_]= If[n==1, 6, Prime[n]*(Prime[n]^2 -1)/2];
Table[a[n], {n,40}]
Join[{6}, Table[Prime[n] (Prime[n]^2 - 1)/2, {n, 2, 40}]] (* Vincenzo Librandi, Sep 29 2015 *)

PARI

a(n) = prime(n)*(prime(n)^2-1)/2;
vector(40, n, a(n+1)) \\ Altug Alkan, Sep 28 2015

SageMath

def A117762(n): return nth_prime(n)*(nth_prime(n)^2-1)/2 + 3*int(n==1)
[A117762(n) for n in range(1,41)] # G. C. Greubel, Jul 21 2023

Formula

a(n) = A127918(n), n>1.

a(n) = A000040(n)*A084921(n). - R. J. Mathar, Jan 29 2024