Explicit sieve estimates and nonexistence of odd multiperfect numbers of a certain form
Number Theory
2024-08-13 v4
Abstract
We prove explicit asymptotic formulae for some functions used in sieve methods and show that there exists no odd multiperfect number of abundancy four whose squared part is cubefree.
Keywords
Cite
@article{arxiv.2103.16936,
title = {Explicit sieve estimates and nonexistence of odd multiperfect numbers of a certain form},
author = {Tomohiro Yamada},
journal= {arXiv preprint arXiv:2103.16936},
year = {2024}
}
Comments
17 pages (The proof of Lemma 2.3 is refined and Theorem 3.1 is improved, freeing us from checking exceptional primes), the author's final version. Appeared in International J. Number Theory (Online Ready)