A285299 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^3 for some prime p.

1, 8, 2, 4, 6, 9, 3, 16, 5, 24, 7, 27, 10, 12, 14, 20, 18, 15, 25, 30, 28, 22, 32, 11, 40, 13, 48, 17, 54, 19, 56, 21, 36, 26, 44, 34, 52, 38, 60, 42, 45, 33, 63, 39, 64, 23, 72, 29, 80, 31, 81, 35, 49, 70, 50, 55, 75, 65, 88, 37, 96, 41, 104, 43, 108, 46, 68

Offset

1,2

Comments

This sequence is a permutation of the natural numbers.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, C++ program for A285299

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the primes p such that p^3 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       8       2
3       2       2
4       4       2
5       6       3
6       9       3
7       3       2
8       16      2
9       5       2
10      24      2
11      7       3
12      27      3
13      10      2
14      12      2
15      14      2
16      20      2
17      18      3
18      15      5
19      25      5
20      30      2
...
64      43      3
65      108     2, 3
66      46      2
...

Crossrefs

Cf. A285296.

Sequence in context: A342261 A010520 A169847 * A073440 A245533 A021552

Adjacent sequences: A285296 A285297 A285298 * A285300 A285301 A285302

Keyword

nonn

Author

Rémy Sigrist, Apr 16 2017

Status

approved