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%I #26 Mar 22 2019 07:58:36
%S 0,1,1,3,6,35,120,105,1120,19089,362880,133595,39916800,148397535,
%T 458313856,2027025,1307674368000,6133352225,355687428096000,
%U 40549021532019,4139906028544000,464463124401214575,51090942171709440000,1173011341727225
%N Number of maximal classes determined by permutations.
%C Corresponds to r_2(k) in the Rosenberg paper.
%H Alois P. Heinz, <a href="/A246069/b246069.txt">Table of n, a(n) for n = 1..450</a>
%H Ivo Rosenberg, <a href="http://dx.doi.org/10.1016/0097-3165(73)90058-7">The number of maximal closed classes in the set of functions over a finite domain</a>, J. Combinatorial Theory Ser. A 14 (1973), 1-7.
%H Ivo Rosenberg and N. J. A. Sloane, <a href="/A002824/a002824_1.pdf">Correspondence, 1971</a>
%F a(n) = sum(n! / (m! * p^m * (p-1)), n = p * m, p prime). (corrected by _Robert Israel_, Aug 27 2014)
%p a:= n -> add(n!/((n/p)! * p^(n/p) * (p-1)), p = numtheory:-factorset(n)):
%p seq(a(n), n=1..100); # _Robert Israel_, Aug 27 2014
%t a[n_] := If[n == 1, 0, Sum[n!/((n/p)! p^(n/p) (p-1)), {p, FactorInteger[n][[All, 1]]}]]; Array[a, 100] (* _Jean-François Alcover_, Mar 22 2019, after _Robert Israel_ *)
%Y Cf. A002826.
%K nonn
%O 1,4
%A _Sean A. Irvine_, Aug 25 2014