a9418a1fe9
* fix: clean-up Project Euler 221-240 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
50 lines
937 B
Markdown
50 lines
937 B
Markdown
---
|
||
id: 5900f4491000cf542c50ff5c
|
||
title: 'Problem 221: Alexandrian Integers'
|
||
challengeType: 5
|
||
forumTopicId: 301864
|
||
dashedName: problem-221-alexandrian-integers
|
||
---
|
||
|
||
# --description--
|
||
|
||
We shall call a positive integer $A$ an "Alexandrian integer", if there exist integers $p$, $q$, $r$ such that:
|
||
|
||
$$A = p \times q \times r$$
|
||
|
||
and
|
||
|
||
$$\frac{1}{A} = \frac{1}{p} + \frac{1}{q} + \frac{1}{r}$$
|
||
|
||
|
||
For example, 630 is an Alexandrian integer ($p = 5$, $q = −7$, $r = −18$). In fact, 630 is the 6th Alexandrian integer, the first 6 Alexandrian integers being: 6, 42, 120, 156, 420 and 630.
|
||
|
||
Find the 150000th Alexandrian integer.
|
||
|
||
# --hints--
|
||
|
||
`alexandrianIntegers()` should return `1884161251122450`.
|
||
|
||
```js
|
||
assert.strictEqual(alexandrianIntegers(), 1884161251122450);
|
||
```
|
||
|
||
# --seed--
|
||
|
||
## --seed-contents--
|
||
|
||
```js
|
||
function alexandrianIntegers() {
|
||
|
||
return true;
|
||
}
|
||
|
||
alexandrianIntegers();
|
||
```
|
||
|
||
# --solutions--
|
||
|
||
```js
|
||
// solution required
|
||
```
|