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---
id: 5900f4491000cf542c50ff5c
title: 'Problem 221: Alexandrian Integers'
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challengeType: 5
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forumTopicId: 301864
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dashedName: problem-221-alexandrian-integers
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---
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# --description--
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We shall call a positive integer $A$ an "Alexandrian integer", if there exist integers $p$, $q$, $r$ such that:
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$$A = p \times q \times r$$
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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.
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Find the 150000th Alexandrian integer.
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# --hints--
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`alexandrianIntegers()` should return `1884161251122450` .
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```js
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assert.strictEqual(alexandrianIntegers(), 1884161251122450);
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```
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# --seed--
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## --seed-contents--
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```js
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function alexandrianIntegers() {
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return true;
}
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alexandrianIntegers();
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```
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# --solutions--
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```js
// solution required
```