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

2,1

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.

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)

Example

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.

Prog

(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

Crossrefs

Cf. A000793.

Sequence in context: A265564 A064764 A340267 * A206398 A000793 A252650

Adjacent sequences: A123128 A123129 A123130 * A123132 A123133 A123134

Keyword

nonn

Author

Antoine Verroken and Vladeta Jovovic, Sep 30 2006

Status

approved