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

2, 3, 4, 6, 6, 12, 15, 20, 30, 30, 60, 42, 84, 105, 140, 210, 210, 420, 280, 420, 420, 840, 504, 1260, 1155, 1540, 2310, 2520, 4620, 3080, 5460, 4620, 9240, 5544, 13860, 9240, 16380, 15015, 27720, 30030, 32760, 60060, 40040, 60060, 60060, 120120, 72072, 180180

Offset: 2

Author

Antoine Verroken and Vladeta Jovovic, Sep 30 2006

Keywords

• nonn

Examples

			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.
For n=26 we have a(26)=1155 since 26 = 3 + 5 + 7 + 11 and lcm([3,5,7,11]) = 1155.
		

Links

• Gheorghe Coserea, Table of n, a(n) for n = 2..124
• Gheorghe Coserea, Partitions solutions for n = 2..124
• J.-L. Nicolas, Ordre maximal d’un élément du groupe S_n des permutations et «highly composite numbers», Bull. Math. Soc. France, 97 (1969), 129-191.

Crossrefs

Cf. A000793.

Programs

PARI

seq(N) = {
  my(a = vector(N+1,n,n));
  for (n=5, #a, forpart(p=n, a[n] = max(a[n],lcm(Vec(p))), [2, n-2]));
  a[2..#a];
};
seq(48) \\ Gheorghe Coserea, Dec 22 2017

Formula

From Gheorghe Coserea, Dec 24 2017: (Start)

A000793(n-2) <= a(n) <= A000793(n), for all n >= 4.

If A000793(n-1) < A000793(n) then a(n) = A000793(n).

(End)