This is a pretty run of the mill question. I will define a sequence and you golf some code to output a entry given a index.
The first item in the sequence is 2.
The nth item in the sequence is the smallest positive integer other than n and 1 sharing at least one factor with n (other than 1) that has not already appeared in the list.
Test cases
Here are the first 25 items in the sequence:
1 2
2 4
3 6
4 8
5 10
6 3
7 14
8 12
9 15
10 5
11 22
12 9
13 26
14 7
15 18
16 20
17 34
18 16
19 38
20 24
21 27
22 11
23 46
24 21
25 30