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A127917
Product of three numbers: n-th prime, previous number, and following number.
15
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
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.
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
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Feb 06 2007
STATUS
approved