Alexandrian Integers
Problem 221
Published on Saturday, 13th December 2008, 01:00 pm; Solved by 1364; Difficulty rating: 65%We shall call a positive integer A an "Alexandrian integer", if there exist integers p, q, r such that:
A = p · q · r and 

= 

+ 

+ 

For example, 630 is an Alexandrian integer (p = 5, q = −7, r = −18). In fact, 630 is the 6^{th} Alexandrian integer, the first 6 Alexandrian integers being: 6, 42, 120, 156, 420 and 630.
Find the 150000^{th} Alexandrian integer.