Problem 124 of Project Euler deals with radical functions, something I have never heard of before. So that always makes it interesting. It reads
The radical of n, rad(n), is the product of distinct prime factors of n. For example, 504 = 23 x 32 x 7, so rad(504) = 2 x 3 x 7 = 42.
If we calculate rad(n) for 1 ≤ n ≤ 10, then sort them on rad(n), and sorting on n if the radical values are equal, we get:
|
Unsorted
|
Sorted
|
||||
 n |
rad(n) |
|
n |
rad(n) |
k |
|
1
|
1
|
1
|
1
|
1
|
|
|
2
|
2
|
2
|
2
|
2
|
|
|
3
|
3
|
4
|
2
|
3
|
|
|
4
|
2
|
8
|
2
|
4
|
|
|
5
|
5
|
3
|
3
|
5
|
|
|
6
|
6
|
9
|
3
|
6
|
|
|
7
|
7
|
5
|
5
|
7
|
|
|
8
|
2
|
6
|
6
|
8
|
|
|
9
|
3
|
7
|
7
|
9
|
|
|
10
|
10
|
10
|
10
|
10
|
|
Let E(k) be the kth element in the sorted n column; for example, E(4) = 8 and E(6) = 9.
If rad(n) is sorted for 1 ≤ n ≤ 100000, find E(10000). Continue reading →
