Refactorable number

This article defines a property that can be evaluated for a natural number, i.e., every natural number either satisfies the property or does not satisfy the property.
View a complete list of properties of natural numbers

Definition

A natural number $n$ is termed refactorable if the value of the divisor count function (i.e., the number of positive divisors) ${\sigma }_0(n)$ divides $n$.

Occurrence

The ID of the sequence in the Online Encyclopedia of Integer Sequences is A033950

Initial values

The first few refactorable numbers are $1,2,8,9,12,18,24,36,\dots$.

Facts

• There do not exist three consecutive refactorable numbers (this was conjectured by Colton and proved by Ore).