

A285575


Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^2 for at least two distinct primes p.


2



1, 36, 2, 18, 4, 9, 8, 25, 12, 3, 24, 6, 30, 10, 20, 5, 40, 15, 45, 16, 27, 28, 7, 56, 14, 42, 21, 48, 33, 44, 11, 72, 13, 52, 26, 50, 22, 54, 32, 49, 60, 35, 63, 64, 75, 39, 78, 66, 84, 51, 68, 17, 100, 19, 76, 38, 90, 34, 98, 46, 92, 23, 108, 29, 116, 58
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OFFSET

1,2


COMMENTS

The sequence can always be extended with a multiple of 36; after a multiple of 36, we can extend the sequence with the least unused number; as there are infinitely many multiples of 36, this sequence is a permutation of the natural numbers (with inverse A285576).
For any k>=0, let c_k be the lexicographically earliest sequence of distinct terms such that the product of two consecutive terms is divisible by p^2 for at least k distinct primes p; in particular we have:
 c_0 = A000027 (the natural numbers),
 c_1 = A285296,
 c_2 = a (this sequence).
For any k>=0, c_k is a permutation of the natural numbers.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, PARI program for A285575
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

The first terms, alongside the primes p such that p^2 divides a(n)*a(n+1), are:
n a(n) p
  
1 1 2, 3
2 36 2, 3
3 2 2, 3
4 18 2, 3
5 4 2, 3
6 9 2, 3
7 8 2, 5
8 25 2, 5
9 12 2, 3
10 3 2, 3
11 24 2, 3
12 6 2, 3
13 30 2, 5
14 10 2, 5
15 20 2, 5
16 5 2, 5
17 40 2, 5
18 15 3, 5
19 45 2, 3
20 16 2, 3
...
115 160 2, 5
116 115 2, 3, 5
117 180 2, 3
...


CROSSREFS

Cf. A285296, A285576 (inverse).
Sequence in context: A330084 A037935 A159824 * A227168 A100252 A020340
Adjacent sequences: A285572 A285573 A285574 * A285576 A285577 A285578


KEYWORD

nonn,look


AUTHOR

Rémy Sigrist, Apr 22 2017


STATUS

approved



