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A285744 Lexicographically earliest sequence of distinct positive terms such that, for any n>0, n*a(n) has at least 5 distinct prime factors.

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