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.

Title	refactorable number
Canonical name	RefactorableNumber
Date of creation	2013-03-22 17:40:41
Last modified on	2013-03-22 17:40:41
Owner	CompositeFan (12809)
Last modified by	CompositeFan (12809)
Numerical id	4
Author	CompositeFan (12809)
Entry type	Definition
Classification	msc 11A25