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143 lines
2.8 KiB
Markdown
143 lines
2.8 KiB
Markdown
---
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id: 5900f3e81000cf542c50fefb
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title: 'Задача 124: Впорядковані радикали'
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challengeType: 1
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forumTopicId: 301751
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dashedName: problem-124-ordered-radicals
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---
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# --description--
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The radical of $n$, $rad(n)$, is the product of the distinct prime factors of $n$. Наприклад, $ 504 = 2^3 × 3^2 × 7 $, тому $rad(504) = 2 × 3 × 7 = 42$.
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Якщо ми обчислюємо $rad (n)$ для $1 ≤ n ≤ 10$, то сортуємо їх за $rad (n)$, а за $n$, якщо радикальні значення рівні, то отримуємо:
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<div style="text-align: center;">
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<table cellpadding="2" cellspacing="0" border="0" align="center">
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<tbody>
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<tr>
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<td colspan="2">$Unsorted$</td>
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<td></td>
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<td colspan="3">$Sorted$</td>
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</tr>
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<tr>
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<td>$n$</td>
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<td>$rad(n)$</td>
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<td></td>
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<td>$n$</td>
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<td>$rad(n)$</td>
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<td>$k$</td>
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</tr>
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<tr>
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<td>1</td>
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<td>1</td>
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<td></td>
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<td>1</td>
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<td>1</td>
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<td>1</td>
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</tr>
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<tr>
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<td>2</td>
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<td>2</td>
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<td></td>
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<td>2</td>
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<td>2</td>
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<td>2</td>
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</tr>
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<tr>
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<td>3</td>
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<td>3</td>
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<td></td>
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<td>4</td>
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<td>2</td>
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<td>3</td>
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</tr>
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<tr>
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<td>4</td>
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<td>2</td>
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<td></td>
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<td>8</td>
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<td>2</td>
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<td>4</td>
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</tr>
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<tr>
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<td>5</td>
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<td>5</td>
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<td></td>
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<td>3</td>
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<td>3</td>
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<td>5</td>
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</tr>
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<tr>
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<td>6</td>
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<td>6</td>
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<td></td>
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<td>9</td>
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<td>3</td>
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<td>6</td>
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</tr>
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<tr>
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<td>7</td>
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<td>7</td>
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<td></td>
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<td>5</td>
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<td>5</td>
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<td>7</td>
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</tr>
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<tr>
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<td>8</td>
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<td>2</td>
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<td></td>
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<td>6</td>
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<td>6</td>
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<td>8</td>
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</tr>
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<tr>
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<td>9</td>
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<td>3</td>
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<td></td>
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<td>7</td>
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<td>7</td>
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<td>9</td>
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</tr>
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<tr>
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<td>10</td>
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<td>10</td>
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<td></td>
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<td>10</td>
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<td>10</td>
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<td>10</td>
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</tr>
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</tbody>
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</table>
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</div><br>
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Нехай $E(k)$ - елемент $k$ у відсортованому стовпці $n$; наприклад, $E(4) = 8$ і $E(6) = 9$. Якщо $rad(n)$ відсортовано за $1 ≤ n ≤ 100000$, знайдіть $E(10000)$.
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# --hints--
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`orderedRadicals()` має повернути `21417`.
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```js
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assert.strictEqual(orderedRadicals(), 21417);
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```
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# --seed--
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## --seed-contents--
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```js
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function orderedRadicals() {
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return true;
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}
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orderedRadicals();
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```
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# --solutions--
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```js
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// solution required
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```
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