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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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Existence of equation about the product of the divisor sum function
Let $\sigma_k(n)$ be the sum of the $k$-th powers of the positive divisors of $n$ and $\mu(n)$ be the Möbius function.
As Arithmetic function - Wikipedia mentioned, there is an equation that $$\sigma …