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%I #19 Jun 14 2024 22:31:08
%S 5348063769211699200,480860607452861427947598643200,
%T 78099458182389588115529148326215680000,
%U 25761093646334667714843750000000000000000000,85057500275967538647136529625446531799449748111360000
%N Order of simple Chevalley group A_7(q), q = prime power.
%D J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker and R. A. Wilson, ATLAS of Finite Groups. Oxford Univ. Press, 1985 [for best online version see https://oeis.org/wiki/Welcome#Links_to_Other_Sites], p. xvi.
%D H. S. M. Coxeter and W. O. J. Moser, Generators and Relations for Discrete Groups, 4th ed., Springer-Verlag, NY, reprinted 1984, p. 131.
%F a(n) = a(A000961(n+1),7) where a(q,n) is defined in A003793. - _Sean A. Irvine_, Sep 18 2015
%t f[m_, n_] := Block[{g, x, y}, g[x_, y_] := x^(y (y + 1)/2) Product[x^k - 1, {k, 2, y + 1}]; g[m, n]/GCD[n + 1, m - 1]]; f[#, 7] & /@ Select[Range[2, 7], PrimePowerQ] (* _Michael De Vlieger_, Sep 18 2015 *)
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_
%E a(5) from _Sean A. Irvine_, Sep 18 2015
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