freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-302-strong-achilles...

---
id: 5900f49b1000cf542c50ffad
title: 'Problem 302: Strong Achilles Numbers'
challengeType: 5
forumTopicId: 301956
dashedName: problem-302-strong-achilles-numbers
---

# --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
```
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`---`
			`id: 5900f49b1000cf542c50ffad`
			`title: 'Problem 302: Strong Achilles Numbers'`
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`challengeType: 5`
fix(curriculum): Added forumTopicId to remaining 1200 challeng… (#36558) 2019-08-05 16:17:33 +00:00			`forumTopicId: 301956`
feat(curriculum): restore seed + solution to Chinese (#40683) * feat(tools): add seed/solution restore script * chore(curriculum): remove empty sections' markers * chore(curriculum): add seed + solution to Chinese * chore: remove old formatter * fix: update getChallenges parse translated challenges separately, without reference to the source * chore(curriculum): add dashedName to English * chore(curriculum): add dashedName to Chinese * refactor: remove unused challenge property 'name' * fix: relax dashedName requirement * fix: stray tag Remove stray `pre` tag from challenge file. Signed-off-by: nhcarrigan <nhcarrigan@gmail.com> Co-authored-by: nhcarrigan <nhcarrigan@gmail.com> 2021-01-13 02:31:00 +00:00			`dashedName: problem-302-strong-achilles-numbers`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`---`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --description--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`A positive integer n is powerful if p2 is a divisor of n for every prime factor p in n.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			`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.`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`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.`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			`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.`

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --hints--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`euler302()` should return 1170060.
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			```js
			`assert.strictEqual(euler302(), 1170060);`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --seed--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`## --seed-contents--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			```js
			`function euler302() {`
fix: remove Good luck! comment from challenge seed code (#39575) 2020-09-15 16:57:40 +00:00
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00			`return true;`
			`}`

			`euler302();`
			```

Feat: add new Markdown parser (#39800) and change all the challenges to new `md` format. 2020-11-27 18:02:05 +00:00			`# --solutions--`
feat(challenge-md): Add initial markdown challenge files 2018-09-30 22:01:58 +00:00
			```js
			`// solution required`
			```