<abstract xmlns="http://www.w3.org/1999/xhtml"> We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function β defined by β(pa) = pa − pa−1 + pa−2 − · · · + (−1)a for every prime power pa (a ≥ 1), and extended by multiplicativity. Certain open problems are also stated.</abstract>

We survey arithmetic and asymptotic properties of the alternating sum-of-divisors function β defined by β(pa) = pa − pa−1 + pa−2 − · · · + (−1)a for every prime power pa (a ≥ 1), and extended by multiplicativity. Certain open problems are also stated.

A survey of the alternating sum-of-divisors function

Universität für Bodenkultur, Institute of Mathematics Department of Integrative Biology Gregor Mendel-Straße 33, A-1180 Wien, Austria / University of Pécs, Department of Mathematics Ifjúság u. 6, H-7624 Pécs, Hungary

Acta Universitatis Sapientiae, Mathematica

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

{"article-title":"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(pa) = pa − pa−1 + pa−2 − · · · + (−1)a for every...

A survey of the alternating sum-of-divisors function

Published Online: Jun 06, 2014

Page range: 93 - 107

Received: Oct 13, 2012

DOI: https://doi.org/10.2478/ausm-2014-0007

Keywords
sum-of-divisors function, Liouville function, Euler’s totient function, specially multiplicative function, imperfect number

© 2014

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

A survey of the alternating sum-of-divisors function

Published Online: Jun 06, 2014

Page range: 93 - 107

Received: Oct 13, 2012

DOI: https://doi.org/10.2478/ausm-2014-0007

Keywordssum-of-divisors function, Liouville function, Euler’s totient function, specially multiplicative function, imperfect number

© 2014

This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.

Keywords
sum-of-divisors function, Liouville function, Euler’s totient function, specially multiplicative function, imperfect number