A002809 Increasing values of A000793 (largest order of permutation of n elements). (Formerly M0577 N0210)

1, 2, 3, 4, 6, 12, 15, 20, 30, 60, 84, 105, 140, 210, 420, 840, 1260, 1540, 2310, 2520, 4620, 5460, 9240, 13860, 16380, 27720, 30030, 32760, 60060, 120120, 180180, 360360, 471240, 510510, 556920, 1021020, 1141140, 2042040, 3063060, 3423420, 6126120, 6846840

Offset

1,2

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000 (first 3318 terms from Alois P. Heinz)

Marc Deléglise and Jean-Louis Nicolas, Maximal product of primes whose sum is bounded, arXiv preprint arXiv:1207.0603 [math.NT], 2012. - From N. J. A. Sloane, Dec 17 2012

J.-L. Nicolas, Sur l'ordre maximum d'un élément dans le groupe S_n des permutations, Acta Arith., 14 (1968), 315-332.

J.-L. Nicolas, Ordre maximal d'un élément du groupe S_n de permutations et 'highly composite numbers', Bull. Math. Soc. France 97 (1969) 129-191.

Mathematica

b[n_, i_] := b[n, i] = Module[{p}, p = If[i<1, 1, Prime[i]]; If[n == 0 || i<1, 1, Max[b[n, i-1], Table[p^j*b[n-p^j, i-1], {j, 1, Log[p, n] // Floor}]]]]; a[n_] := b[n, If[n<8, 3, PrimePi[Ceiling[1.328*Sqrt[n*Log[n] // Floor]]]]]; Table[a[n], {n, 0, 100}] // Union (* Jean-François Alcover, Mar 07 2014, after Alois P. Heinz *)

Crossrefs

Indices are A006644.

Cf. A000793.

Sequence in context: A057919 A102250 A084788 * A015904 A015888 A339793

Adjacent sequences: A002806 A002807 A002808 * A002810 A002811 A002812

Keyword

nonn,nice

Author

N. J. A. Sloane

Extensions

Description improved Apr 15 1997. More terms from David W. Wilson.

Status

approved