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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. 2
 2310, 1155, 770, 1365, 462, 385, 330, 1785, 910, 231, 210, 455, 420, 165, 154, 1995, 390, 595, 510, 273, 110, 105, 546, 665, 714, 255, 1190, 195, 570, 77, 630, 2145, 70, 285, 66, 715, 660, 315, 140, 357, 690, 55, 780, 345, 182, 399, 798, 805, 858, 429, 130 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. The inverse of this sequence is the sequence itself. 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). Conjecturally, a(n) ~ n. 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. LINKS Rémy Sigrist, Table of n, a(n) for n = 1..25000 Rémy Sigrist, PARI program for A285744 Rémy Sigrist, Colored scatterplot of the first 25000 terms EXAMPLE The first terms, alongside the primes p dividing n*a(n), are: n       a(n)    p --      ----    -------------- 1       2310    2, 3, 5, 7, 11 2       1155    2, 3, 5, 7, 11 3       770     2, 3, 5, 7, 11 4       1365    2, 3, 5, 7,     13 5       462     2, 3, 5, 7, 11 6       385     2, 3, 5, 7, 11 7       330     2, 3, 5, 7, 11 8       1785    2, 3, 5, 7,         17 9       910     2, 3, 5, 7,     13 10      231     2, 3, 5, 7, 11 11      210     2, 3, 5, 7, 11 12      455     2, 3, 5, 7,     13 13      420     2, 3, 5, 7,     13 14      165     2, 3, 5, 7, 11 15      154     2, 3, 5, 7, 11 16      1995    2, 3, 5, 7,             19 17      390     2, 3, 5,        13, 17 18      595     2, 3, 5, 7,         17 19      510     2, 3, 5,            17, 19 20      273     2, 3, 5, 7,     13 CROSSREFS Cf. A285487. Sequence in context: A280659 A060231 A285487 * A051270 A046387 A136154 Adjacent sequences:  A285741 A285742 A285743 * A285745 A285746 A285747 KEYWORD nonn,look AUTHOR Rémy Sigrist, Apr 25 2017 STATUS approved

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Last modified February 25 02:54 EST 2020. Contains 332217 sequences. (Running on oeis4.)