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An arithmetic function is one whose domain is the positive integers and whose range is a subset of the complex numbers. There are a number of important number-theoretic examples.

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For which $n$ is $\sum_{k=1}^n 1 / \varphi(k)$ an integer?

For which positive integers $n$ is the sum $\sum_{k=1}^n 1 / \varphi(k)$ an integer? Here $\varphi$ is the Euler totient function. The question is a "totient-analog" of the well-known result that $\su …