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A182606 Number of conjugacy classes in GL(n,13).

%I A182606 #25 Jun 19 2023 09:03:04
%S A182606 1,12,168,2184,28548,371112,4826640,62746152,815728368,10604468628,
%T A182606 137858461104,1792159992168,23298084722808,302875101365928,
%U A182606 3937376380474992,51185892946146672,665416609115237772,8650415918497693704,112455406951074120024
%N A182606 Number of conjugacy classes in GL(n,13).
%H A182606 Alois P. Heinz, <a href="/A182606/b182606.txt">Table of n, a(n) for n = 0..300</a>
%F A182606 G.f.: Product_{k>=1} (1-x^k)/(1-13*x^k). - _Alois P. Heinz_, Nov 03 2012
%p A182606 with(numtheory):
%p A182606 b:= proc(n) b(n):= add(phi(d)*13^(n/d), d=divisors(n))/n-1 end:
%p A182606 a:= proc(n) a(n):= `if`(n=0, 1,
%p A182606        add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p A182606     end:
%p A182606 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 03 2012
%t A182606 b[n_] := Sum[EulerPhi[d]*13^(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, 30}] (* _Jean-François Alcover_, Feb 17 2014, after _Alois P. Heinz_ *)
%o A182606 (Magma) /* The program does not work for n>5: */ [1] cat [NumberOfClasses(GL(n, 13)): n in [1..5]];
%o A182606 (PARI)
%o A182606 N=66; x='x+O('x^N);
%o A182606 gf=prod(n=1,N, (1-x^n)/(1-13*x^n)  );
%o A182606 v=Vec(gf)
%o A182606 /* _Joerg Arndt_, Jan 24 2013 */
%Y A182606 Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182607, A182608, A182609, A182610, A182611, A182612.
%K A182606 nonn
%O A182606 0,2
%A A182606 _Klaus Brockhaus_, Nov 23 2010
%E A182606 More terms from _Alois P. Heinz_, Nov 03 2012
%E A182606 MAGMA code edited by _Vincenzo Librandi_, Jan 24 2013