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A285744
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Lexicographically earliest sequence of distinct positive terms such that, for any n>0, n*a(n) has at least 5 distinct prime factors.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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