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

1,1

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.

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)

Mathematica

Table[(Prime[n] + 1) Prime[n](Prime[n] - 1), {n, 1, 100}]

Prog

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

Crossrefs

Cf. A036689, A034953, A084920, A117762.

Cf. A065470, A065487.

Sequence in context: A109583 A352807 A100934 * A293118 A293121 A026982

Adjacent sequences: A127914 A127915 A127916 * A127918 A127919 A127920

Keyword

nonn,easy

Author

Artur Jasinski, Feb 06 2007

Status

approved