---
id: 5900f49b1000cf542c50ffad
challengeType: 5
title: 'Problem 302: Strong Achilles Numbers'
---

## Description
<section id='description'>
A positive integer n is powerful if p2 is a divisor of n for every prime factor p in n.


A positive integer n is a perfect power if n can be expressed as a power of another positive integer.


A positive integer n is an Achilles number if n is powerful but not a perfect power. For example, 864 and 1800 are Achilles numbers: 864 = 25·33 and 1800 = 23·32·52.


We shall call a positive integer S a Strong Achilles number if both S and φ(S) are Achilles numbers.1
For example, 864 is a Strong Achilles number: φ(864) = 288 = 25·32. However, 1800 isn't a Strong Achilles number because: φ(1800) = 480 = 25·31·51.

There are 7 Strong Achilles numbers below 104 and 656 below 108.


How many Strong Achilles numbers are there below 1018?


1 φ denotes Euler's totient function.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler302()</code> should return 1170060.
    testString: assert.strictEqual(euler302(), 1170060);

```

</section>

## Challenge Seed
<section id='challengeSeed'>

<div id='js-seed'>

```js
function euler302() {
  // Good luck!
  return true;
}

euler302();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>