---
id: 5900f3e81000cf542c50fefb
title: 'Problema 124: radicali ordinati'
challengeType: 1
forumTopicId: 301751
dashedName: problem-124-ordered-radicals
---

# --description--

Il radicale di $n$, $rad(n)$, è il prodotto dei fattori distinti primi di $n$. Per esempio, $504 = 2^3 ×3^2 × 7$, quindi $rad(504) = 2 × 3 × 7 = 42$.

Se calcoliamo $rad(n)$ for $1 ≤ n ≤ 10$,, quindi ordiniamo su $rad(n)$, e ordiniamo su $n$ se i valori dei radicali sono uguali, otteniamo:

<div style="text-align: center;">
  <table cellpadding="2" cellspacing="0" border="0" align="center">
    <tbody>
      <tr>
        <td colspan="2">$non in ordine$</td>
        <td></td>
        <td colspan="3">$ordinato$</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><br>

Sia $E(k)$ l'elemento $k$-simo nella colonna $n$ ordinata; per esempio, $E(4) = 8$ e $E(6) = 9$. Se $rad(n)$ è ordinato per $1 ≤ n ≤ 100000$, trova $E(10000)$.

# --hints--

`orderedRadicals()` dovrebbe restituire `21417`.

```js
assert.strictEqual(orderedRadicals(), 21417);
```

# --seed--

## --seed-contents--

```js
function orderedRadicals() {

  return true;
}

orderedRadicals();
```

# --solutions--

```js
// solution required
```
