A survey of the alternating sum-of-divisors function

We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function $β$ defined by $β(p^a)=p^a-p^{a-1}+p^{a-2}-...+(-1)^a$ for every prime power $p^a$ ($a\ge 1$), and extended by multiplicativity. Certain open problems are also stated.

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