Generalizing Abundancy Index to Gaussian Integers

zbMATH Open1441.11272arXiv2004.13487MaRDI QIDQ3303775

Author name not available (Why is that?)

Publication date: 4 August 2020

Abstract: Abundancy index refers to the ratio of the sum of the divisors of a number to the number itself. It is a concept of great importance in defining friendly and perfect numbers. Here, we describe a suitable generalization of abundancy index to the ring of Gaussian integers ($mathbbZ[i]$). We first show that this generalization possesses many of the useful properties of the traditional abundancy index in $mathbbZ$. We then investigate $k$-powerful $au$-perfect numbers and prove results regarding their existence in $mathbbZ[i]$.

Full work available at URL: https://arxiv.org/abs/2004.13487

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: Generalizing Abundancy Index to Gaussian Integers

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q3303775)