---
id: 5900f3e81000cf542c50fefb
challengeType: 5
title: 'Problem 124: Ordered radicals'
---
## Description
The radical of n, rad(n), is the product of the distinct prime factors of n. For example, 504 = 23 × 32 × 7, so rad(504) = 2 × 3 × 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
11
111
22
222
33
423
42
824
55
335
66
936
77
557
82
668
93
779
1010
101010
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).
## Instructions
## Tests
```yml
tests:
- text: euler124() should return 21417.
testString: assert.strictEqual(euler124(), 21417);
```
## Challenge Seed
```js
function euler124() {
// Good luck!
return true;
}
euler124();
```