# Problem 221: Alexandrian Integers

![graphic](img221.gif)

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.