Unitary divisor

In mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and ${\displaystyle {\frac {b}{a}}}$ are coprime, having no common factor other than 1. Equivalently, a divisor a of b is a unitary divisor if and only if every prime factor of a has the same multiplicity in a as it has in b.

The concept of a unitary divisor originates from R. Vaidyanathaswamy (1931),^[1] who used the term block divisor.