Refactorable number

A refactorable number or tau number is an integer n that is divisible by the count of its divisors, or to put it algebraically, n is such that ${\displaystyle \tau (n)\mid n}$ with ${\displaystyle \tau (n)=\sigma _{0}(n)=\prod _{i=1}^{n}(e_{i}+1)}$ for ${\displaystyle n=\prod _{i=1}^{n}p_{i}^{e_{i}}}$. The first few refactorable numbers are listed in (sequence A033950 in the OEIS) as

1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96, 104, 108, 128, 132, 136, 152, 156, 180, 184, 204, 225, 228, 232, 240, 248, 252, 276, 288, 296, ...

For example, 18 has 6 divisors (1 and 18, 2 and 9, 3 and 6) and is divisible by 6. There are infinitely many refactorable numbers.