100 lines
1.2 KiB
Markdown
100 lines
1.2 KiB
Markdown
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---
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id: 5900f3b11000cf542c50fec4
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challengeType: 5
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title: 'Problem 69: Totient maximum'
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---
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## Description
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<section id='description'>
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Euler's Totient function, φ(n) [sometimes called the phi function], is used to determine the number of numbers less than n which are relatively prime to n. For example, as 1, 2, 4, 5, 7, and 8, are all less than nine and relatively prime to nine, φ(9)=6.
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n
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Relatively Prime
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φ(n)
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n/φ(n)
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2
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1
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1
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2
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3
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1,2
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2
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1.5
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4
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1,3
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2
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2
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5
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1,2,3,4
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4
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1.25
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6
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1,5
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2
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3
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7
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1,2,3,4,5,6
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6
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1.1666...
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8
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1,3,5,7
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4
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2
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9
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1,2,4,5,7,8
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6
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1.5
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10
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1,3,7,9
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4
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2.5
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It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10.
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Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.
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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>euler69()</code> should return 510510.
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testString: 'assert.strictEqual(euler69(), 510510, ''<code>euler69()</code> should return 510510.'');'
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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 euler69() {
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// Good luck!
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return true;
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}
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euler69();
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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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