DE-BUNDESWETTBEWERB 2021 Problem 2

The fraction $\frac{3}{10}$ can be written as a sum of two reciprocals in exactly two ways: $$\frac{3}{10}=\frac{1}{5}+\frac{1}{10}=\frac{1}{4}+\frac{1}{20}$$ a) In how many ways can $\frac{3}{2021}$ be written as a sum of two reciprocals? b) Is there a positive integer $n$ not divisible by $3$ with the property that $\frac{3}{n}$ can be written as a sum of two reciprocals in exactly $2021$ ways?