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Mobius inversion formula

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Suppose that $f$ and $g$ are functions from the natural numbers to the real numbers such that $f(n) = \sum_{d|n}g(d)$. Then we can express $g$ in terms of $f$ as $g(n) = \sum_{d|n} \mu(\frac{n}{d})f(d)$ where $\mu$ is the Mobius function. This formula is useful in number theory.

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