43 lines
818 B
Markdown
43 lines
818 B
Markdown
---
|
||
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
|
||
```
|