cp's OEIS Frontend

A182610 Number of conjugacy classes in GL(n,23).

%I A182610 #25 Jun 19 2023 12:12:49
%S A182610 1,22,528,12144,279818,6435792,148035360,3404812752,78310972608,
%T A182610 1801152369478,41426510921664,952809751186128,21914624425304688,
%U A182610 504036361781716368,11592836324384010432,266635235460831961152,6132610415677439376122,141050039560581098947824
%N A182610 Number of conjugacy classes in GL(n,23).
%H A182610 Alois P. Heinz, <a href="/A182610/b182610.txt">Table of n, a(n) for n = 0..250</a>
%F A182610 G.f.: Product_{k>=1} (1-x^k)/(1-23*x^k). - _Alois P. Heinz_, Nov 03 2012
%p A182610 with(numtheory):
%p A182610 b:= proc(n) b(n):= add(phi(d)*23^(n/d), d=divisors(n))/n-1 end:
%p A182610 a:= proc(n) a(n):= `if`(n=0, 1,
%p A182610        add(add(d*b(d), d=divisors(j)) *a(n-j), j=1..n)/n)
%p A182610     end:
%p A182610 seq(a(n), n=0..20);  # _Alois P. Heinz_, Nov 03 2012
%t A182610 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_ *)
%o A182610 (Magma) /* The program does not work for n>4: */ [1] cat [NumberOfClasses(GL(n, 23)) : n in [1..4]];
%o A182610 (PARI)
%o A182610 N=66; x='x+O('x^N);
%o A182610 gf=prod(n=1,N, (1-x^n)/(1-23*x^n)  );
%o A182610 v=Vec(gf)
%o A182610 /* _Joerg Arndt_, Jan 24 2013 */
%Y A182610 Cf. A006951, A006952, A049314, A049315, A049316, A182603, A182604, A182605, A182606, A182607, A182608, A182609, A182611, A182612.
%K A182610 nonn
%O A182610 0,2
%A A182610 _Klaus Brockhaus_, Nov 23 2010
%E A182610 More terms from _Alois P. Heinz_, Nov 03 2012
%E A182610 MAGMA code edited by _Vincenzo Librandi_, Jan 24 2013