#!/usr/bin/env python
# coding=utf-8

"""598. Split Divisibilities
https://projecteuler.net/problem=598

Consider the number 48.  
There are five pairs of integers $a$ and $b$ ($a \leq b$) such that $a \times
b=48$: (1,48), (2,24), (3,16), (4,12) and (6,8).  
It can be seen that both 6 and 8 have 4 divisors.  
So of those five pairs one consists of two integers with the same number of
divisors.

In general:  
Let $C(n)$ be the number of pairs of positive integers $a \times b=n$, ($a
\leq b$) such that $a$ and $b$ have the same number of divisors;  
so $C(48)=1$.
You are given $C(10!)=3$: (1680, 2160), (1800, 2016) and (1890,1920).

Find $C(100!)$
"""