## Alexandrian Integers

### Problem 221

Published on Saturday, 13th December 2008, 01:00 pm; Solved by 1162

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

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.