Question 120
Let $N$ be the number of triples of positive integers $(a, b, c)$ satisfying
$$
a \leq b \leq c, \quad \operatorname{gcd}(a, b, c)=1, \quad a b c=6^{2020}
$$
Compute the remainder when $N$ is divided by 1000.
$$
a \leq b \leq c, \quad \operatorname{gcd}(a, b, c)=1, \quad a b c=6^{2020}
$$
Compute the remainder when $N$ is divided by 1000.