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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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 18 07:05 EDT 2024. Contains 375996 sequences. (Running on oeis4.)