A285386 Lexicographically earliest sequence of distinct positive terms such that the product of two consecutive terms is divisible by p^4 for some prime p.

1, 16, 2, 8, 4, 12, 20, 24, 6, 27, 3, 32, 5, 48, 7, 64, 9, 18, 36, 28, 40, 10, 56, 14, 72, 22, 80, 11, 81, 13, 96, 15, 54, 21, 108, 30, 88, 26, 104, 34, 112, 17, 128, 19, 144, 23, 160, 25, 50, 75, 100, 44, 52, 60, 68, 76, 84, 92, 116, 120, 38, 136, 42, 135, 33

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 A285386

Rémy Sigrist, Scatterplot of the first 100000 terms

Index entries for sequences that are permutations of the natural numbers

Example

The first terms, alongside the primes p such that p^4 divides a(n)*a(n+1), are:
n       a(n)    p
--      ----    -
1       1       2
2       16      2
3       2       2
4       8       2
5       4       2
6       12      2
7       20      2
8       24      2
9       6       3
10      27      3
11      3       2
12      32      2
13      5       2
14      48      2
15      7       2
16      64      2
17      9       3
18      18      3
19      36      2
20      28      2
...
165     95      2
166     432     2, 3
167     87      3
...

Crossrefs

Cf. A285296.

Sequence in context: A040253 A180730 A040254 * A100079 A144532 A270570

Adjacent sequences: A285383 A285384 A285385 * A285387 A285388 A285389

Keyword

nonn

Author

Rémy Sigrist, Apr 18 2017

Status

approved