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