2022-01-20 19:30:18 +00:00
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---
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id: 5900f5411000cf542c510054
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2022-01-22 15:08:20 +00:00
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title: '問題 468: 二項係数の Smooth 約数'
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2022-07-12 11:56:02 +00:00
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challengeType: 1
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2022-01-20 19:30:18 +00:00
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forumTopicId: 302143
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dashedName: problem-468-smooth-divisors-of-binomial-coefficients
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---
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# --description--
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2022-01-22 15:08:20 +00:00
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$B$ より大きい素因数を持たない整数は B-smooth と呼ばれます。
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2022-01-20 19:30:18 +00:00
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2022-01-22 15:08:20 +00:00
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$n$ の最大の B-smooth 約数を $SB(n)$ とします。
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2022-01-20 19:30:18 +00:00
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2022-01-22 15:08:20 +00:00
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例:
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2022-01-20 19:30:18 +00:00
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2022-04-02 08:46:30 +00:00
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$$\begin{align} & S_1(10) = 1 \\\\
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& S_4(2\\,100) = 12 \\\\ & S_{17}(2\\,496\\,144) = 5\\,712 \end{align}$$
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2022-01-20 19:30:18 +00:00
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2022-01-22 15:08:20 +00:00
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$F(n) = \displaystyle\sum_{B = 1}^n \sum_{r = 0}^n S_B(\displaystyle\binom{n}{r})$ と定義します。 ここで、$\displaystyle\binom{n}{r}$ は二項係数を表します。
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2022-01-20 19:30:18 +00:00
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2022-01-22 15:08:20 +00:00
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例:
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2022-01-20 19:30:18 +00:00
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2022-04-02 08:46:30 +00:00
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$$\begin{align} & F(11) = 3132 \\\\
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& F(1\\,111)\bmod 1\\,000\\,000\\,993 = 706\\,036\\,312 \\\\ & F(111\\,111)\bmod 1\\,000\\,000\\,993 = 22\\,156\\,169 \end{align}$$
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2022-01-20 19:30:18 +00:00
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2022-01-22 15:08:20 +00:00
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$F(11\\,111\\,111)\bmod 1\\,000\\,000\\,993$ を求めなさい。
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2022-01-20 19:30:18 +00:00
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# --hints--
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2022-01-22 15:08:20 +00:00
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`smoothDivisorsOfBinomialCoefficients()` は `852950321` を返す必要があります。
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2022-01-20 19:30:18 +00:00
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```js
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assert.strictEqual(smoothDivisorsOfBinomialCoefficients(), 852950321);
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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 smoothDivisorsOfBinomialCoefficients() {
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return true;
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}
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smoothDivisorsOfBinomialCoefficients();
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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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