45 lines
899 B
Markdown
45 lines
899 B
Markdown
---
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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. Examples: S1(10) = 1 S4(2100) = 12 S17(2496144) = 5712
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Define F(n) = ∑1≤B≤n ∑0≤r≤n SB(C(n,r)). Here, C(n,r) denotes the binomial coefficient. Examples: F(11) = 3132 F(1 111) mod 1 000 000 993 = 706036312 F(111 111) mod 1 000 000 993 = 22156169
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Find F(11 111 111) mod 1 000 000 993.
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# --hints--
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`euler468()` should return 852950321.
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```js
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assert.strictEqual(euler468(), 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 euler468() {
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return true;
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}
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euler468();
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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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