143 lines
2.8 KiB
Markdown
143 lines
2.8 KiB
Markdown
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---
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id: 5900f3e81000cf542c50fefb
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title: '問題 124: 順序付き累乗根'
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challengeType: 5
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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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$n$ の累乗根 $rad(n)$ は、$n$ の相異なる素因数の積です。 例えば、$504 = 2^3 × 3^2 × 7$ なので、$rad(504) = 2 × 3 × 7 = 42$ です。
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$1 ≤ n ≤ 10$ に対して $rad(n)$ を求め、それらを $rad(n)$ でソートし、累乗根の値が等しい場合は $n$ でソートすると、次のようになります。
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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">$未ソート$</td>
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<td></td>
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<td colspan="3">$ソート済み$</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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ソート済みの $n$ 列の $k$ 番目の要素を $E(k)$ とします。例えば、$E(4) = 8$, $E(6) = 9$ です。 $1 ≤ n ≤ 100000$ のとき、$rad(n)$ をソートした場合の $E(10000)$ を求めなさい。
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# --hints--
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`orderedRadicals()` は `21417` を返す必要があります。
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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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```
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