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 $\tau (n)|n$, with $\tau (n)$ being the divisor function. The first few refactorable numbers are listed in the OEIS A033950 are 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96. The equation $\gcd (n,x)=\tau (n)$ has solutions only if $n$ is a refactorable number.