A064797 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, where p_{n+1} = p_1.

1, 2, 6, 6, 12, 12, 15, 15, 18, 18, 24, 24, 35, 35, 35, 35, 44, 44, 55, 55, 55, 55, 68, 68, 68, 68, 68, 68, 85, 85, 102, 102, 102, 102, 102, 102, 119, 119, 119, 119, 145, 145, 174, 174, 174, 174, 203, 203, 203, 203, 203, 203, 232, 232, 232, 232, 232, 232, 261, 261

Offset: 1

Author

N. J. A. Sloane, Oct 21 2001

Keywords

• nonn
• nice

Comments

Testing a trial value of a(n) is equivalent to searching for a Hamiltonian cycle in the appropriate graph. - Martin Fuller, Jul 30 2006

Examples

			n=4: we must arrange the numbers 1..4 in a circle so that the max of the lcm of pairs of adjacent terms is minimized. The answer is 1423, with max lcm = 6, so a(4) = 6.
		

Crossrefs

Cf. A064764, A035106, A064796, A000720, A073818.

Programs

Mathematica

Table[Min[Max[LCM@@@Partition[#,2,1,1]]&/@Permutations[Range[n]]], {n,10}] (* Harvey P. Dale, Oct 05 2011 *) (* The program takes a long time to run and uses a great deal of memory *)

Formula

For n >= 3, a(n) >= A073818(pi(n)+1), with equality for 17 <= n <= 250 - Martin Fuller, Jul 30 2006

Extensions

More terms from Vladeta Jovovic, Oct 22 2001

a(11)-a(24) from Charles R Greathouse IV, Jul 23 2006

More terms from Martin Fuller, Jul 30 2006