Powers of 2

Define \(f(n)\) to be equal to the greatest power of \(2\) that \(n\) is divisible by. For instance, \(f(5)=1\) and \(f(12)=4\). If \(f(1)+f(2)+\cdots+f(n)=1000\), find \(n\).

Source: AoPS
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