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%I #12 Jun 20 2017 23:53:04
%S 1,1260,2,630,4,315,8,180,7,240,6,210,10,126,16,90,14,120,12,105,20,
%T 63,32,45,28,60,21,80,18,70,24,75,36,35,48,30,42,40,54,50,66,56,72,25,
%U 84,15,96,33,100,27,112,39,132,49,108,44,117,64,81,88,78,98,99
%N Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms has at least 34 divisors.
%C The number of divisors is given by A000005.
%C This sequence is a permutation of the natural numbers, with inverse A288922.
%C Conjecturally, a(n) ~ n.
%C See also A288923 for similar sequences.
%H Rémy Sigrist, <a href="/A288921/b288921.txt">Table of n, a(n) for n = 1..30000</a>
%H Rémy Sigrist, <a href="/A288921/a288921.gp.txt">PARI program for A288921</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The first terms, alongside a(n)*a(n+1) and its number of divisors, are:
%e n a(n) a(n)*a(n+1) Number of divisors
%e -- ---- ----------- ------------------
%e 1 1 1260 36
%e 2 1260 2520 48
%e 3 2 1260 36
%e 4 630 2520 48
%e 5 4 1260 36
%e 6 315 2520 48
%e 7 8 1440 36
%e 8 180 1260 36
%e 9 7 1680 40
%e 10 240 1440 36
%e 11 6 1260 36
%e 12 210 2100 36
%e 13 10 1260 36
%e 14 126 2016 36
%e 15 16 1440 36
%e 16 90 1260 36
%e 17 14 1680 40
%e 18 120 1440 36
%e 19 12 1260 36
%e 20 105 2100 36
%Y Cf. A000005, A288922 (inverse), A288923.
%K nonn,look
%O 1,2
%A _Rémy Sigrist_, Jun 19 2017
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