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

Author

Rémy Sigrist, Apr 16 2017

Keywords

• nonn

Comments

This sequence is a permutation of the natural numbers.

Examples

			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
...
		

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

Crossrefs

Cf. A285296.