

A123131


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


2



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
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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), 129191.


FORMULA

From Gheorghe Coserea, Dec 24 2017: (Start)
A000793(n2) <= a(n) <= A000793(n), for all n >= 4.
If A000793(n1) < 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, n2]));
a[2..#a];
};
seq(48) \\ Gheorghe Coserea, Dec 22 2017


CROSSREFS

Cf. A000793.
Sequence in context: A210733 A265564 A064764 * A206398 A000793 A252650
Adjacent sequences: A123128 A123129 A123130 * A123132 A123133 A123134


KEYWORD

nonn


AUTHOR

Antoine Verroken and Vladeta Jovovic, Sep 30 2006


STATUS

approved



