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A182612 Number of conjugacy classes in GL(n,27).

%I A182612 #22 Sep 08 2022 08:45:55
%S A182612 1,26,728,19656,531414,14348152,387419760,10460332792,282429516096,
%T A182612 7625596933890,205891131543552,5559060551656248,150094635282119528,
%U A182612 4052555152616676888,109418989131110078784,2954312706539971597184,79766443076861647780830
%N A182612 Number of conjugacy classes in GL(n,27).
%H A182612 Alois P. Heinz, <a href="/A182612/b182612.txt">Table of n, a(n) for n = 0..250</a>
%F A182612 G.f.: Product_{k>=1} (1-x^k)/(1-27*x^k). - _Alois P. Heinz_, Nov 03 2012
%p A182612 with(numtheory):
%p A182612 b:= proc(n) b(n):= add(phi(d)*27^(n/d), d=divisors(n))/n-1 end:
%p A182612 a:= proc(n) a(n):= `if`(n=0, 1,
%p A182612        add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p A182612     end:
%p A182612 seq(a(n), n=0..20);  # _Alois P. Heinz_, Nov 03 2012
%t A182612 b[n_] := Sum[EulerPhi[d]*27^(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_ *)
%o A182612 (Magma) /* The program does not work for n>4: */ [1] cat [ NumberOfClasses(GL(n, 27)) : n in [1..4] ];
%o A182612 (PARI)
%o A182612 N=66; x='x+O('x^N);
%o A182612 gf=prod(n=1,N, (1-x^n)/(1-27*x^n)  );
%o A182612 v=Vec(gf)
%o A182612 /* _Joerg Arndt_, Jan 24 2013 */
%Y A182612 Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182610, A182611.
%K A182612 nonn
%O A182612 0,2
%A A182612 _Klaus Brockhaus_, Nov 23 2010
%E A182612 More terms from _Alois P. Heinz_, Nov 03 2012
%E A182612 MAGMA code edited by _Vincenzo Librandi_, Jan 24 2013