---
id: 5900f45d1000cf542c50ff70
challengeType: 5
title: '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.
## Instructions
## Tests
```yml
tests:
- text: euler241() should return 482316491800641150.
testString: assert.strictEqual(euler241(), 482316491800641150, 'euler241() should return 482316491800641150.');
```
## Challenge Seed
```js
function euler241() {
// Good luck!
return true;
}
euler241();
```