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A123131 Largest order of permutations of n elements with no fixed points.

%I A123131 #32 Dec 27 2017 03:21:41
%S A123131 2,3,4,6,6,12,15,20,30,30,60,42,84,105,140,210,210,420,280,420,420,
%T A123131 840,504,1260,1155,1540,2310,2520,4620,3080,5460,4620,9240,5544,13860,
%U A123131 9240,16380,15015,27720,30030,32760,60060,40040,60060,60060,120120,72072,180180
%N A123131 Largest order of permutations of n elements with no fixed points.
%H A123131 Gheorghe Coserea, <a href="/A123131/b123131.txt">Table of n, a(n) for n = 2..124</a>
%H A123131 Gheorghe Coserea, <a href="/A123131/a123131.txt">Partitions solutions for n = 2..124</a>
%H A123131 J.-L. Nicolas, <a href="http://eudml.org/doc/87121">Ordre maximal d’un élément du groupe S_n des permutations et «highly composite numbers»</a>, Bull. Math. Soc. France, 97 (1969), 129-191.
%F A123131 From _Gheorghe Coserea_, Dec 24 2017: (Start)
%F A123131 A000793(n-2) <= a(n) <= A000793(n), for all n >= 4.
%F A123131 If A000793(n-1) < A000793(n) then a(n) = A000793(n).
%F A123131 (End)
%e A123131 For n=22 we have a(22)=420 since 22 = 4 + 5 + 6 + 7 = 3 + 3 + 4 + 5 + 7 and lcm([4, 5, 6, 7]) = lcm([3, 3, 4, 5, 7]) = 420.
%e A123131 For n=26 we have a(26)=1155 since 26 = 3 + 5 + 7 + 11 and lcm([3,5,7,11]) = 1155.
%o A123131 (PARI)
%o A123131 seq(N) = {
%o A123131   my(a = vector(N+1,n,n));
%o A123131   for (n=5, #a, forpart(p=n, a[n] = max(a[n],lcm(Vec(p))), [2, n-2]));
%o A123131   a[2..#a];
%o A123131 };
%o A123131 seq(48) \\ _Gheorghe Coserea_, Dec 22 2017
%Y A123131 Cf. A000793.
%K A123131 nonn
%O A123131 2,1
%A A123131 Antoine Verroken and _Vladeta Jovovic_, Sep 30 2006