---
id: 5900f49b1000cf542c50ffad
title: 'Problem 302: Strong Achilles Numbers'
challengeType: 5
forumTopicId: 301956
---

# --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.

# --hints--

`euler302()` should return 1170060.

```js
assert.strictEqual(euler302(), 1170060);
```

# --seed--

## --seed-contents--

```js
function euler302() {

  return true;
}

euler302();
```

# --solutions--

```js
// solution required
```