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%I #11 Apr 26 2017 23:21:21
%S 2310,1155,770,1365,462,385,330,1785,910,231,210,455,420,165,154,1995,
%T 390,595,510,273,110,105,546,665,714,255,1190,195,570,77,630,2145,70,
%U 285,66,715,660,315,140,357,690,55,780,345,182,399,798,805,858,429,130
%N Lexicographically earliest sequence of distinct positive terms such that, for any n>0, n*a(n) has at least 5 distinct prime factors.
%C If n has at least 5 distinct prime factors, then a(n) is the least unused number; as there are infinitely many numbers with at least 5 distinct prime factors, this sequence is a permutation of the natural numbers.
%C The inverse of this sequence is the sequence itself.
%C The first fixed points are: 40755, 42966, 54285, 54740, 55965, 56070, 66045, 66066, 70035, 70350, 73815, 73920 (note that the fixed points have at least 5 distinct prime factors).
%C Conjecturally, a(n) ~ n.
%C This sequence has similarities with A285487: here n*a(n) has at least 5 distinct prime factors, there a(n)*a(n+1) has at least 5 distinct prime factors.
%H Rémy Sigrist, <a href="/A285744/b285744.txt">Table of n, a(n) for n = 1..25000</a>
%H Rémy Sigrist, <a href="/A285744/a285744.gp.txt">PARI program for A285744</a>
%H Rémy Sigrist, <a href="/A285744/a285744.png">Colored scatterplot of the first 25000 terms</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%e The first terms, alongside the primes p dividing n*a(n), are:
%e n a(n) p
%e -- ---- --------------
%e 1 2310 2, 3, 5, 7, 11
%e 2 1155 2, 3, 5, 7, 11
%e 3 770 2, 3, 5, 7, 11
%e 4 1365 2, 3, 5, 7, 13
%e 5 462 2, 3, 5, 7, 11
%e 6 385 2, 3, 5, 7, 11
%e 7 330 2, 3, 5, 7, 11
%e 8 1785 2, 3, 5, 7, 17
%e 9 910 2, 3, 5, 7, 13
%e 10 231 2, 3, 5, 7, 11
%e 11 210 2, 3, 5, 7, 11
%e 12 455 2, 3, 5, 7, 13
%e 13 420 2, 3, 5, 7, 13
%e 14 165 2, 3, 5, 7, 11
%e 15 154 2, 3, 5, 7, 11
%e 16 1995 2, 3, 5, 7, 19
%e 17 390 2, 3, 5, 13, 17
%e 18 595 2, 3, 5, 7, 17
%e 19 510 2, 3, 5, 17, 19
%e 20 273 2, 3, 5, 7, 13
%Y Cf. A285487.
%K nonn,look
%O 1,1
%A _Rémy Sigrist_, Apr 25 2017