# refactorable number

A 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.

Title refactorable number RefactorableNumber 2013-03-22 17:40:41 2013-03-22 17:40:41 CompositeFan (12809) CompositeFan (12809) 4 CompositeFan (12809) Definition msc 11A25