76 lines
1.4 KiB
Markdown
76 lines
1.4 KiB
Markdown
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---
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id: 5
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localeTitle: 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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La función de Möbius, denotada μ (n), se define como:
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μ (n) = (-1) ω (n) si n es squarefree (donde ω (n) es el número de factores primos distintos de n)
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μ (n) = 0 si n no es squarefree.
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Sea P (a, b) el número de enteros n en el intervalo [a, b] tal que μ (n) = 1.
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Sea N (a, b) el número de enteros n en el intervalo [ a, b] tal que μ (n) = -1.
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Por ejemplo, P (2,10) = 2 y N (2,10) = 4.
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Sea C (n) el número de pares de enteros (a, b) de manera que:
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1 ≤ a ≤ b ≤ n,
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99 · N (a, b) ≤ 100 · P (a, b) y
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99 · P (a, b) ≤ 100 · N (a, b).
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Por ejemplo, C (10) = 13, C (500) = 16676 y C (10 000) = 20155319.
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Encuentre 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> debe devolver 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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