We shall call a positive integer A an "Alexandrian integer", if there exist integers p, q, r such that:

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.