# 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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