A064764 Largest integer m such that every permutation (p_1, ..., p_n) of (1, ..., n) satisfies lcm(p_i, p_{i+1}) >= m for some i, 1 <= i <= n-1.

1, 2, 3, 4, 6, 6, 12, 12, 12, 12, 18, 18, 24, 24, 24, 24, 35, 35, 44, 44, 44, 44, 55, 55, 55, 55, 55, 55, 68, 68, 85, 85, 85, 85, 85, 85, 102, 102, 102, 102, 119, 119, 145, 145, 145, 145, 174, 174, 174, 174, 174, 174, 203, 203, 203, 203, 203, 203, 232, 232, 261, 261, 261

Offset

1,2

Comments

For n >= 4, a(n) >= A073818(pi(n)), with equality for 19 <= n <= 70. - David Wasserman, Aug 17 2002

Links

Table of n, a(n) for n=1..63.

P. Erdős, R. Freud, and N. Hegyvári, Arithmetical properties of permutations of integers, Acta Mathematica Hungarica 41:1-2 (1983), pp 169-176.

D. Wasserman, Proof of terms 11-70

Formula

a(n) = (1+o(1))n^2/(4 log n) as n -> infinity.

Example

n=6: we must arrange the numbers 1..6 so that the max of the lcm of pairs of adjacent terms is minimized. The answer is 632415, with max lcm = 6, so a(6) = 6.

Crossrefs

Cf. A035106, A064736, A064796, A064797, A000720, A073818.

Sequence in context: A007464 A210733 A265564 * A340267 A123131 A206398

Adjacent sequences: A064761 A064762 A064763 * A064765 A064766 A064767

Keyword

nonn,nice

Author

N. J. A. Sloane, Oct 21 2001

Extensions

More terms from Vladeta Jovovic, Oct 21 2001

Further terms from David Wasserman, Aug 17 2002

Status

approved