curriculum/challenges/english/blocks/project-euler-problems-101-to-200/5900f3e81000cf542c50fefb.md
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:
<div style="text-align: center;"> <table cellpadding="2" cellspacing="0" border="0" align="center"> <tbody> <tr> <td colspan="2">$Unsorted$</td> <td></td> <td colspan="3">$Sorted$</td> </tr> <tr> <td>$n$</td> <td>$rad(n)$</td> <td></td> <td>$n$</td> <td>$rad(n)$</td> <td>$k$</td> </tr> <tr> <td>1</td> <td>1</td> <td></td> <td>1</td> <td>1</td> <td>1</td> </tr> <tr> <td>2</td> <td>2</td> <td></td> <td>2</td> <td>2</td> <td>2</td> </tr> <tr> <td>3</td> <td>3</td> <td></td> <td>4</td> <td>2</td> <td>3</td> </tr> <tr> <td>4</td> <td>2</td> <td></td> <td>8</td> <td>2</td> <td>4</td> </tr> <tr> <td>5</td> <td>5</td> <td></td> <td>3</td> <td>3</td> <td>5</td> </tr> <tr> <td>6</td> <td>6</td> <td></td> <td>9</td> <td>3</td> <td>6</td> </tr> <tr> <td>7</td> <td>7</td> <td></td> <td>5</td> <td>5</td> <td>7</td> </tr> <tr> <td>8</td> <td>2</td> <td></td> <td>6</td> <td>6</td> <td>8</td> </tr> <tr> <td>9</td> <td>3</td> <td></td> <td>7</td> <td>7</td> <td>9</td> </tr> <tr> <td>10</td> <td>10</td> <td></td> <td>10</td> <td>10</td> <td>10</td> </tr> </tbody> </table> </div>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 $E(10000)$.
orderedRadicals() should return 21417.
assert.strictEqual(orderedRadicals(), 21417);
function orderedRadicals() {
return true;
}
orderedRadicals();
// solution required