A survey of the alternating sum-of-divisors function

László Tóth

A survey of the alternating sum-of-divisors function

Number Theory 2014-01-28 v2

Authors: László Tóth

Abstract

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.

Keywords

alternating sum-of-divisors multiplicative function arithmetic properties asymptotic properties prime power

Cite

@article{arxiv.1111.4842,
  title  = {A survey of the alternating sum-of-divisors function},
  author = {László Tóth},
  journal= {arXiv preprint arXiv:1111.4842},
  year   = {2014}
}

Comments

Dedicated to the memory of my friend and colleague, Professor Antal Bege (1962-2012), 11 pages

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