# Problem 598: Split Divisibilities
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!)\$