A survey of the alternating sum-of-divisors function

Details A survey of the alternating sum-of-divisors function A survey of the alternating sum-of-divisors function

2011-11-21

arxiv.org/abs/1111.4842v1

Mathematics

Number Theory

11 pages

Scientific paper

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

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