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%I A127917 #43 Nov 22 2022 02:34:59
%S A127917 6,24,120,336,1320,2184,4896,6840,12144,24360,29760,50616,68880,79464,
%T A127917 103776,148824,205320,226920,300696,357840,388944,492960,571704,
%U A127917 704880,912576,1030200,1092624,1224936,1294920,1442784,2048256,2247960,2571216,2685480,3307800
%N A127917 Product of three numbers: n-th prime, previous number, and following number.
%C A127917 a(n) is the order of the matrix group SL(2,prime(n)). - _Tom Edgar_, Sep 28 2015
%H A127917 G. C. Greubel, <a href="/A127917/b127917.txt">Table of n, a(n) for n = 1..10000</a>
%H A127917 J. B. Marshall, <a href="https://doi.org/10.1017/S0013091500024536">On the extension of Fermat's theorem to matrices of order n</a>, Proceedings of the Edinburgh Mathematical Society 6 (1939) 85-91. See (11) page 90-91 when p=2.
%H A127917 <a href="/index/Pri#prime_powers">Index to sequences related to prime powers</a>.
%F A127917 a(n) = prime(n)*(prime(n)^2-1). - _Tom Edgar_, Sep 28 2015
%F A127917 a(n) = 2 * A117762(n), for n > 1. - _Altug Alkan_, Sep 28 2015
%F A127917 From _Amiram Eldar_, Nov 22 2022: (Start)
%F A127917 Product_{n>=1} (1 + 1/a(n)) = A065487.
%F A127917 Product_{n>=1} (1 - 1/a(n)) = A065470. (End)
%t A127917 Table[(Prime[n] + 1) Prime[n](Prime[n] - 1), {n, 1, 100}]
%o A127917 (PARI) forprime(p=2,1e3,print1(6*binomial(p+1,3)", ")) \\ _Charles R Greathouse IV_, Jun 16 2011
%o A127917 (PARI) a(n) = prime(n)*(prime(n)^2-1);
%o A127917 vector(40, n, a(n)) \\ _Altug Alkan_, Sep 28 2015
%o A127917 (Magma) [6] cat [NthPrime(n)*(NthPrime(n)^2-1): n in [2..40]]; // _Vincenzo Librandi_, Sep 29 2015
%Y A127917 Cf. A036689, A034953, A084920, A117762.
%Y A127917 Cf. A065470, A065487.
%K A127917 nonn,easy
%O A127917 1,1
%A A127917 _Artur Jasinski_, Feb 06 2007

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