A refactorable number (or tau number) is divisible by its own count of divisors. For example, 12 has six divisors (1, 2, 3, 4, 6, 12), and 12 is divisible by 6 — so 12 is refactorable. The sequence: 1, 2, 8, 9, 12, 18, 24, 36, 40, 56, 60, 72, 80, 84, 88, 96.
They were studied by Curtis Cooper and Robert Kennedy, who proved that no three consecutive integers can all be refactorable. An old conjecture of theirs — that arbitrarily long runs of refactorable numbers in arithmetic progression exist — connects to deep questions about the distribution of divisor counts.