75 lines
1.3 KiB
Markdown
75 lines
1.3 KiB
Markdown
---
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id: 5900f53d1000cf542c51004f
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challengeType: 5
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title: 'Problem 464: Möbius function and intervals'
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---
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## Description
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<section id='description'>
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The Möbius function, denoted μ(n), is defined as:
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μ(n) = (-1)ω(n) if n is squarefree (where ω(n) is the number of distinct prime factors of n)
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μ(n) = 0 if n is not squarefree.
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Let P(a,b) be the number of integers n in the interval [a,b] such that μ(n) = 1.
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Let N(a,b) be the number of integers n in the interval [a,b] such that μ(n) = -1.
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For example, P(2,10) = 2 and N(2,10) = 4.
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Let C(n) be the number of integer pairs (a,b) such that:
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1 ≤ a ≤ b ≤ n,
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99·N(a,b) ≤ 100·P(a,b), and
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99·P(a,b) ≤ 100·N(a,b).
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For example, C(10) = 13, C(500) = 16676 and C(10 000) = 20155319.
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Find C(20 000 000).
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</section>
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## Instructions
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<section id='instructions'>
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</section>
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## Tests
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<section id='tests'>
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```yml
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tests:
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- text: <code>euler464()</code> should return 198775297232878.
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testString: assert.strictEqual(euler464(), 198775297232878, '<code>euler464()</code> should return 198775297232878.');
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```
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</section>
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## Challenge Seed
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<section id='challengeSeed'>
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<div id='js-seed'>
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```js
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function euler464() {
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// Good luck!
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return true;
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}
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euler464();
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```
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</div>
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</section>
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## Solution
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<section id='solution'>
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```js
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// solution required
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```
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</section>
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