100 lines
1.2 KiB
Markdown
100 lines
1.2 KiB
Markdown
---
|
|
id: 5900f3b11000cf542c50fec4
|
|
challengeType: 5
|
|
title: 'Problem 69: Totient maximum'
|
|
---
|
|
|
|
## Description
|
|
<section id='description'>
|
|
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.
|
|
|
|
n
|
|
Relatively Prime
|
|
φ(n)
|
|
n/φ(n)
|
|
2
|
|
1
|
|
1
|
|
2
|
|
3
|
|
1,2
|
|
2
|
|
1.5
|
|
4
|
|
1,3
|
|
2
|
|
2
|
|
5
|
|
1,2,3,4
|
|
4
|
|
1.25
|
|
6
|
|
1,5
|
|
2
|
|
3
|
|
7
|
|
1,2,3,4,5,6
|
|
6
|
|
1.1666...
|
|
8
|
|
1,3,5,7
|
|
4
|
|
2
|
|
9
|
|
1,2,4,5,7,8
|
|
6
|
|
1.5
|
|
10
|
|
1,3,7,9
|
|
4
|
|
2.5
|
|
|
|
It can be seen that n=6 produces a maximum n/φ(n) for n ≤ 10.
|
|
Find the value of n ≤ 1,000,000 for which n/φ(n) is a maximum.
|
|
</section>
|
|
|
|
## Instructions
|
|
<section id='instructions'>
|
|
|
|
</section>
|
|
|
|
## Tests
|
|
<section id='tests'>
|
|
|
|
```yml
|
|
tests:
|
|
- text: <code>euler69()</code> should return 510510.
|
|
testString: assert.strictEqual(euler69(), 510510, '<code>euler69()</code> should return 510510.');
|
|
|
|
```
|
|
|
|
</section>
|
|
|
|
## Challenge Seed
|
|
<section id='challengeSeed'>
|
|
|
|
<div id='js-seed'>
|
|
|
|
```js
|
|
function euler69() {
|
|
// Good luck!
|
|
return true;
|
|
}
|
|
|
|
euler69();
|
|
```
|
|
|
|
</div>
|
|
|
|
|
|
|
|
</section>
|
|
|
|
## Solution
|
|
<section id='solution'>
|
|
|
|
```js
|
|
// solution required
|
|
```
|
|
</section>
|