Refactorable number

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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]. The first few refactorable numbers are listed in (sequence in OEIS)

1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96

The equation GCD(n, x) = τ(n) has solutions only if n is a refactorable number.

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