68 lines
1.2 KiB
Markdown
68 lines
1.2 KiB
Markdown
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---
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id: 5900f4621000cf542c50ff74
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challengeType: 5
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title: 'Problem 245: Coresilience'
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forumTopicId: 301892
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---
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## Description
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<section id='description'>
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We shall call a fraction that cannot be cancelled down a resilient fraction. Furthermore we shall define the resilience of a denominator, R(d), to be the ratio of its proper fractions that are resilient; for example, R(12) = 4⁄11.
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The resilience of a number d > 1 is then
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φ(d)d − 1
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, where φ is Euler's totient function.
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We further define the coresilience of a number n > 1 as C(n)=
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n − φ(n)n − 1.
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The coresilience of a prime p is C(p)
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=
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1p − 1.
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Find the sum of all composite integers 1 < n ≤ 2×1011, for which C(n) is a unit fraction.
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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>euler245()</code> should return 288084712410001.
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testString: assert.strictEqual(euler245(), 288084712410001);
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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 euler245() {
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return true;
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}
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euler245();
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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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