---
id: 5900f45d1000cf542c50ff70
challengeType: 5
title: 'Problem 241: Perfection Quotients'
forumTopicId: 301888
---

## Description
<section id='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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler241()</code> should return 482316491800641150.
    testString: assert.strictEqual(euler241(), 482316491800641150);

```

</section>

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

<div id='js-seed'>

```js
function euler241() {
  // Good luck!
  return true;
}

euler241();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```

</section>