---
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 · q · r and 1/A = 1/p + 1/q + 1/r

<!-- TODO Use MathJax -->

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--

`euler221()` should return 1884161251122450.

```js
assert.strictEqual(euler221(), 1884161251122450);
```

# --seed--

## --seed-contents--

```js
function euler221() {

  return true;
}

euler221();
```

# --solutions--

```js
// solution required
```