# Unitary Divisors

We define a unitary divisor of $$n$$ to be a divisor $$d$$ such that $$\gcd \left(d,\dfrac{n}{d}\right)=1$$. Let $$S$$ be the sum of all unitary divisors of $$2016^{2016}$$. Determine the remainder when $$S$$ is divided by 1000.

 Notation: $$\gcd(\cdot)$$ denotes the greatest common divisor function.

×