Let f be the unique function defined on the positive integers such that
$$\sum_{d \mid n} d \cdot f\left(\dfrac{n}{d}\right)=1$$
for all positive integers n, where the sum is taken over all positive divisors of n. What is f(2023)?
Answer Choices
A. -1536
B. 96
C. 108
D. 116
E. 144