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 A182610 Number of conjugacy classes in GL(n,23). 17
 1, 22, 528, 12144, 279818, 6435792, 148035360, 3404812752, 78310972608, 1801152369478, 41426510921664, 952809751186128, 21914624425304688, 504036361781716368, 11592836324384010432, 266635235460831961152, 6132610415677439376122, 141050039560581098947824 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..250 FORMULA G.f.: Product_{k>=1} (1-x^k)/(1-23*x^k). - Alois P. Heinz, Nov 03 2012 MAPLE with(numtheory): b:= proc(n) b(n):= add(phi(d)*23^(n/d), d=divisors(n))/n-1 end: a:= proc(n) a(n):= `if`(n=0, 1, add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n) end: seq(a(n), n=0..20); # Alois P. Heinz, Nov 03 2012 MATHEMATICA b[n_] := Sum[EulerPhi[d]*23^(n/d), {d, Divisors[n]}]/n-1; a[n_] := a[n] = If[n == 0, 1, Sum[Sum[d*b[d], {d, Divisors[j]}]*a[n-j], {j, 1, n}]/n]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 17 2014, after Alois P. Heinz *) PROG (Magma) /* The program does not work for n>4: */ [1] cat [NumberOfClasses(GL(n, 23)) : n in [1..4]]; (PARI) N=66; x='x+O('x^N); gf=prod(n=1, N, (1-x^n)/(1-23*x^n) ); v=Vec(gf) /* Joerg Arndt, Jan 24 2013 */ CROSSREFS Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182611, A182612. Sequence in context: A158629 A253777 A266884 * A320766 A203456 A271266 Adjacent sequences: A182607 A182608 A182609 * A182611 A182612 A182613 KEYWORD nonn AUTHOR Klaus Brockhaus, Nov 23 2010 EXTENSIONS More terms from Alois P. Heinz, Nov 03 2012 MAGMA code edited by Vincenzo Librandi, Jan 24 2013 STATUS approved

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Last modified June 23 15:55 EDT 2024. Contains 373651 sequences. (Running on oeis4.)