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

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

Author

N. J. A. Sloane

Keywords

• nonn
• nice

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.

Crossrefs

Indices are A006644.

Cf. A000793.

Programs

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 *)

Extensions

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