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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 13 05:41 EDT 2020. Contains 336442 sequences. (Running on oeis4.)