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%I #31 Oct 08 2023 04:44:06
%S 1,16,144,96,1200,144,2352,384,1296,1200,5808,288,8112,2352,3600,1536,
%T 13872,1296,17328,2400,7056,5808,25392,1152,30000,8112,11664,4704,
%U 40368,3600,46128,6144,17424,13872,58800,2592,65712,17328,24336,9600
%N a(1) = 1, a(2) = 16, a(n) = lcm(48, 2n^2) for n>2.
%C In the M. Reid reference the following is proved: Let S(n) be the set of all groups whose order is a product of primes congruent to 1 mod n. Then, a(n) = gcd{|G| - |cc(G)| : G in S(n)}, where |cc(G)| is the number of conjugacy classes of G. - _Eric M. Schmidt_, Apr 18 2013
%H Michael Reid, <a href="http://www.jstor.org/stable/2589713">The number of conjugacy classes</a>, Amer. Math. Monthly, 105 (1998), 359-361.
%H <a href="/index/Rec#order_36">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,0,0,3,0,0,0,0,0,0,0,0,0,0,0,-3,0,0,0,0,0,0,0,0,0,0,0,1).
%H <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%F a(n) = 3a(n-12) - 3a(n-24) + a(n-36) for n > 38. - _Charles R Greathouse IV_, Apr 18 2013
%F Sum_{n>=1} 1/a(n) = 11*Pi^2/1296 + 49/48. - _Amiram Eldar_, Oct 08 2023
%t a[n_] := LCM[48, 2*n^2]; a[1] = 1; a[2] = 16; Array[a, 40] (* _Amiram Eldar_, Oct 08 2023 *)
%o (Magma) [1,16] cat [ LCM(48,2*n^2) : n in [3..10] ]; // Sergei Haller (sergei(AT)sergei-haller.de), Dec 21 2006
%o (PARI) a(n)=if(n>2,lcm(48,2*n^2),15*n-14) \\ _Charles R Greathouse IV_, Apr 18 2013
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E Definition rewritten by _Eric M. Schmidt_, Apr 18 2013
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