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A182603 Number of conjugacy classes in GL(n,8).

%I A182603 #29 Sep 08 2022 08:45:55
%S A182603 1,7,63,504,4088,32697,262080,2096577,16776648,134213128,1073737224,
%T A182603 8589897288,68719439943,549755515008,4398046212672,35184369697407,
%U A182603 281474974319672,2251799794521144,18014398490350584,144115187922510840,1152921504453534648
%N A182603 Number of conjugacy classes in GL(n,8).
%H A182603 Alois P. Heinz, <a href="/A182603/b182603.txt">Table of n, a(n) for n = 0..1000</a>
%F A182603 G.f.: prod((1-x^k)/(1-8*x^k),k=1..infinity).
%p A182603 with(numtheory):
%p A182603 b:= proc(n) b(n):= add(phi(d)*8^(n/d), d=divisors(n))/n-1 end:
%p A182603 a:= proc(n) a(n):= `if`(n=0, 1,
%p A182603        add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p A182603     end:
%p A182603 seq(a(n), n=0..30);  # _Alois P. Heinz_, Nov 03 2012
%t A182603 b[n_] := Sum[EulerPhi[d]*8^(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 A182603 (Magma) /* The program does not work for n>6: */ [1] cat [NumberOfClasses(GL(n, 8)): n in [1..6]];
%Y A182603 Cf. A006951, A006952, A049314, A049315, A049316, A182604 - A182612.
%K A182603 nonn
%O A182603 0,2
%A A182603 _Klaus Brockhaus_, Nov 23 2010
%E A182603 Extended by _D. S. McNeil_, Dec 06 2010
%E A182603 MAGMA code edited by _Vincenzo Librandi_, Jan 23 2013