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A302350 Instance of a permutation of the positive integers such that lcm(a(n), a(n+1)) <= c*n*log(n)^2.

%I A302350 #16 Dec 19 2024 11:46:19
%S A302350 1,6,3,15,30,10,5,20,2,140,35,70,210,105,21,42,14,7,77,154,770,385,55,
%T A302350 110,330,165,33,66,22,11,143,429,858,286,2002,91,273,546,182,910,455,
%U A302350 65,130,390,195,39,78,26,13,221,663,1326,442,4862,187,561,1122,374,2618,119,357,714,238,1190,595,85,170,510,255,51,102,34,17
%N A302350 Instance of a permutation of the positive integers such that lcm(a(n), a(n+1)) <= c*n*log(n)^2.
%C A302350 For details of the construction see [Mazet & Saias].
%C A302350 This sequence is also a "chain": a(n) is either a divisor or a multiple of a(n+1).
%C A302350 Another instance of a "permutation-chain" is: A064736.
%H A302350 Michel Marcus, <a href="/A302350/b302350.txt">Table of n, a(n) for n = 1..5168</a> (for 26 iterations)
%H A302350 Y.-G. Chen and C.-S. Ji, <a href="https://doi.org/10.1007/s10474-011-0099-x">The permutation of integers with small least common multiple of two subsequent terms</a>, Acta Math. Hungarica 132(2011), 307-309.
%H A302350 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 A302350 Michel Marcus, <a href="/A302350/a302350.gp.txt">PARI scripts</a>
%H A302350 Pierre Mazet, Eric Saias, <a href="https://arxiv.org/abs/1803.10073">Etude du graphe divisoriel 4</a>, arXiv:1803.10073 [math.NT], 2018.
%H A302350 G. Tenenbaum, <a href="https://doi.org/10.24033/asens.1502">Sur un problème de crible et ses applications</a>, Annales scientifiques de l'École Normale Supérieure, 4ème série, tome 19, n°1, (1986), p.1-30.
%H A302350 G. Tenenbaum, <a href="https://doi.org/10.24033/asens.1710">Sur un problème de crible et ses applications. II. Corrigendum et étude du graphe divisoriel</a>, Annales scientifiques de l'École Normale Supérieure, Série 4 : Tome 28 (1995) no. 2 , p. 115-127.
%H A302350 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A302350 (PARI) \\ See links.
%Y A302350 Cf. A064736.
%K A302350 nonn
%O A302350 1,2
%A A302350 _Michel Marcus_, Apr 06 2018