---
id: 5900f4491000cf542c50ff5c
challengeType: 5
title: 'Problem 221: Alexandrian Integers'
---

## Description
<section id='description'>
We shall call a positive integer A an "Alexandrian integer", if there exist integers p, q, r such that:


      A = p · q · r    and  


      1A
   =

      1p
   +

      1q
   +

      1r
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.
</section>

## Instructions
<section id='instructions'>

</section>

## Tests
<section id='tests'>

```yml
tests:
  - text: <code>euler221()</code> should return 1884161251122450.
    testString: assert.strictEqual(euler221(), 1884161251122450, '<code>euler221()</code> should return 1884161251122450.');

```

</section>

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

<div id='js-seed'>

```js
function euler221() {
  // Good luck!
  return true;
}

euler221();
```

</div>



</section>

## Solution
<section id='solution'>

```js
// solution required
```
</section>