---
id: 5900f3e81000cf542c50fefb
title: 'Problem 124: Ordered radicals'
challengeType: 5
forumTopicId: 301751
dashedName: problem-124-ordered-radicals
---
# --description--
The radical of $n$, $rad(n)$, is the product of the distinct prime factors of $n$. For example, $504 = 2^3 × 3^2 × 7$, 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:
| $Unsorted$ |
|
$Sorted$ |
| $n$ |
$rad(n)$ |
|
$n$ |
$rad(n)$ |
$k$ |
| 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 $k$th 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 $E(10000)$.
# --hints--
`orderedRadicals()` should return `21417`.
```js
assert.strictEqual(orderedRadicals(), 21417);
```
# --seed--
## --seed-contents--
```js
function orderedRadicals() {
return true;
}
orderedRadicals();
```
# --solutions--
```js
// solution required
```