---
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>