A285417 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^5 for some prime p.

1, 32, 2, 16, 4, 8, 12, 24, 20, 40, 28, 48, 6, 64, 3, 81, 9, 27, 18, 54, 36, 56, 44, 72, 52, 80, 10, 96, 5, 128, 7, 160, 11, 192, 13, 224, 14, 112, 22, 144, 26, 176, 30, 162, 15, 243, 17, 256, 19, 288, 21, 320, 23, 352, 25, 125, 50, 208, 34, 240, 38, 272, 42

Offset: 1

Author

Rémy Sigrist, Apr 18 2017

Keywords

• nonn

Comments

This sequence is a permutation of the natural numbers.

Examples

			The first terms, alongside the primes p such that p^5 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       32      2
3       2       2
4       16      2
5       4       2
6       8       2
7       12      2
8       24      2
9       20      2
10      40      2
11      28      2
12      48      2
13      6       2
14      64      2
15      3       3
16      81      3
17      9       3
18      27      3
19      18      3
20      54      3
...
1476    7744    2
1477    811     2, 3
1478    7776    2, 3
1479    813     3
...
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Rémy Sigrist, C++ program for A285417
• Rémy Sigrist, Scatterplot of the first 150000 terms
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A285296.