freeCodeCamp/curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-241-perfection-quot...

---
id: 5900f45d1000cf542c50ff70
title: 'Problem 241: Perfection Quotients'
challengeType: 5
forumTopicId: 301888
dashedName: problem-241-perfection-quotients
---

# --description--

For a positive integer n, let σ(n) be the sum of all divisors of n, so e.g. σ(6) = 1 + 2 + 3 + 6 = 12.

A perfect number, as you probably know, is a number with σ(n) = 2n.

Let us define the perfection quotient of a positive integer asp(n)= σ(n)n . Find the sum of all positive integers n ≤ 1018 for which p(n) has the form k + 1⁄2, where k is an integer.

# --hints--

`euler241()` should return 482316491800641150.

```js
assert.strictEqual(euler241(), 482316491800641150);
```

# --seed--

## --seed-contents--

```js
function euler241() {

  return true;
}

euler241();
```

# --solutions--

```js
// solution required
```
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
+								---
 								id: 5900f45d1000cf542c50ff70
 								title: 'Problem 241: Perfection Quotients'
-												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: 301888
-												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-241-perfection-quotients
-												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
+								For a positive integer n, let σ(n) be the sum of all divisors of n, so e.g. σ(6) = 1 + 2 + 3 + 6 = 12.
-												feat(challenge-md): Add initial markdown challenge files

											
										
										
											2018-09-30 22:01:58 +00:00
 								A perfect number, as you probably know, is a number with σ(n) = 2n.
-												Feat: add new Markdown parser (#39800)

and change all the challenges to new `md` format.
											
										
										
											2020-11-27 18:02:05 +00:00
+								Let us define the perfection quotient of a positive integer asp(n)= σ(n)n . Find the sum of all positive integers n ≤ 1018 for which p(n) has the form k + 1⁄2, where k is an integer.
-												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
+								# --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
+								`euler241()` should return 482316491800641150.
-												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(euler241(), 482316491800641150);
-												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 euler241() {
-												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;
 								}
 								euler241();
 								```
-												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
 								```