---
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
```