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

Author

N. J. A. Sloane, Oct 21 2001

Keywords

• nonn
• nice

Comments

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

Examples

			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.
		

Links

• 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

Crossrefs

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

Formula

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

Extensions

More terms from Vladeta Jovovic, Oct 21 2001

Further terms from David Wasserman, Aug 17 2002