53 lines
1.2 KiB
Markdown
53 lines
1.2 KiB
Markdown
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---
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id: 5900f5411000cf542c510054
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title: 'Problem 468: Smooth divisors of binomial coefficients'
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challengeType: 5
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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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An integer is called B-smooth if none of its prime factors is greater than $B$.
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Let $SB(n)$ be the largest B-smooth divisor of $n$.
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Examples:
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$$\begin{align} & S_1(10) = 1 \\\\ & S_4(2\\,100) = 12 \\\\ & S_{17}(2\\,496\\,144) = 5\\,712 \end{align}$$
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Define $F(n) = \displaystyle\sum_{B = 1}^n \sum_{r = 0}^n S_B(\displaystyle\binom{n}{r})$. Here, $\displaystyle\binom{n}{r}$ denotes the binomial coefficient.
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Examples:
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$$\begin{align} & F(11) = 3132 \\\\ & F(1\\,111)\bmod 1\\,000\\,000\\,993 = 706\\,036\\,312 \\\\ & F(111\\,111)\bmod 1\\,000\\,000\\,993 = 22\\,156\\,169 \end{align}$$
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Find $F(11\\,111\\,111)\bmod 1\\,000\\,000\\,993$.
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# --hints--
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`smoothDivisorsOfBinomialCoefficients()` should return `852950321`.
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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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