Let $f(n)$ denote the largest odd factor of $n$, including possibly $n$ itself. Determine the value of \[ \frac{f(1)}{1} + \frac{f(2)}{2} + \frac{f(3)}{3} + \cdots + \frac{f(2048)}{2048}, \] rounded to the nearest integer.

Let's think step by step and output the final answer within \boxed{}.
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