A127917 Product of three numbers: n-th prime, previous number, and following number.

6, 24, 120, 336, 1320, 2184, 4896, 6840, 12144, 24360, 29760, 50616, 68880, 79464, 103776, 148824, 205320, 226920, 300696, 357840, 388944, 492960, 571704, 704880, 912576, 1030200, 1092624, 1224936, 1294920, 1442784, 2048256, 2247960, 2571216, 2685480, 3307800

Offset: 1

Author

Artur Jasinski, Feb 06 2007

Keywords

• nonn
• easy

Comments

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

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• J. B. Marshall, On the extension of Fermat's theorem to matrices of order n, Proceedings of the Edinburgh Mathematical Society 6 (1939) 85-91. See (11) page 90-91 when p=2.
• Index to sequences related to prime powers.

Crossrefs

Cf. A036689, A034953, A084920, A117762.

Cf. A065470, A065487.

Programs

Magma

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

Mathematica

Table[(Prime[n] + 1) Prime[n](Prime[n] - 1), {n, 1, 100}]
Table[p(p^2-1),{p,Prime[Range[40]]}] (* Harvey P. Dale, Apr 26 2025 *)

PARI

forprime(p=2,1e3,print1(6*binomial(p+1,3)", ")) \\ Charles R Greathouse IV, Jun 16 2011

PARI

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

Formula

a(n) = prime(n)*(prime(n)^2-1). - Tom Edgar, Sep 28 2015

a(n) = 2 * A117762(n), for n > 1. - Altug Alkan, Sep 28 2015

From Amiram Eldar, Nov 22 2022: (Start)

Product_{n>=1} (1 + 1/a(n)) = A065487.

Product_{n>=1} (1 - 1/a(n)) = A065470. (End)