freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-124-ordered-radicals.english.md

---
id: 5900f3e81000cf542c50fefb
challengeType: 5
title: 'Problem 124: Ordered radicals'
---

## Description
<section id='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).
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler124()</code> should return 21417.
    testString: assert.strictEqual(euler124(), 21417, '<code>euler124()</code> should return 21417.');

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler124() {
  // Good luck!
  return true;
}

euler124();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>