A064764 - OEIS

%I #12 May 07 2018 21:33:55

%S 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,

%T 55,55,55,68,68,85,85,85,85,85,85,102,102,102,102,119,119,145,145,145,

%U 145,174,174,174,174,174,174,203,203,203,203,203,203,232,232,261,261,261

%N 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.

%C For n >= 4, a(n) >= A073818(pi(n)), with equality for 19 <= n <= 70. - _David Wasserman_, Aug 17 2002

%H P. Erdős, R. Freud, and N. Hegyvári, <a href="https://users.renyi.hu/~p_erdos/1983-02.pdf">Arithmetical properties of permutations of integers</a>, Acta Mathematica Hungarica 41:1-2 (1983), pp 169-176.

%H D. Wasserman, <a href="http://home.earthlink.net/~dwasserm/A064764.html">Proof of terms 11-70</a>

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

%e 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.

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

%K nonn,nice

%O 1,2

%A _N. J. A. Sloane_, Oct 21 2001

%E More terms from _Vladeta Jovovic_, Oct 21 2001

%E Further terms from _David Wasserman_, Aug 17 2002