data/problems/221.yml
---
:id: 221
:name: Alexandrian Integers
:url: https://projecteuler.net/problem=221
:content: "We shall call a positive integer <var>A</var> an \"Alexandrian integer\",
if there exist integers <var>p</var>, <var>q</var>, <var>r</var> such that:\n\n|
<var>A</var> = <var>p</var> · <var>q</var> · <var>r</var> and
| \n\n| 1 |\n| <var>A</var> |\n\n | = | \n\n| 1 |\n| <var>p</var> |\n\n | + | \n\n|
1 |\n| <var>q</var> |\n\n | + | \n\n| 1 |\n| <var>r</var> |\n\n |\n\nFor example,
630 is an Alexandrian integer (<var>p</var> = 5, <var>q</var> = −7,
<var>r</var> = −18). In fact, 630 is the 6<sup>th</sup> Alexandrian integer,
the first 6 Alexandrian integers being: 6, 42, 120, 156, 420 and 630.\n\nFind the
150000<sup>th</sup> Alexandrian integer.\n\n"