A new upper bound for odd perfect numbers of a special form

2017/06/30 by Tomohiro Yamada · 1 citation
Computer Science · Engineering · Mathematics · #Computability, Logic, AI Algorithms #Finite Group Theory Research #graph theory and CDMA systems #math.NT #msc:11A05 #msc:11A25 #msc:11D61 #msc:11J86

paper · pdf · doi:10.4064/cm7339-3-2018

published as (v2) Colloq. Math. 156 (2019), 15--23, corrigendum: Colloq. Math. 162 (2020), 311--313 (DOI: 10.4064/cm8138-4-2020) · 10 pages, the author's revised version; 3 pages, corrigendum to the previous (published in the journal) version

openalex publication_date 2018/12/11 · arxiv created 2019/12/31 · arxiv updated 2020/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We shall given a new effectively computable upper bound of odd perfect numbers whose Euler factors are powers of fixed exponent, improving our old result in T. Yamada, Colloq. Math. 103 (2005), 303--307.

Citations

• Untersuchungen über ungerade vollkommene Zahlen.
• Zur Theorie der Potenzreste
• A new result concerning the structure of odd perfect numbers
• The non-existence of odd perfect numbers of a certain form

Cited by

• Perfect number [wikipedia]

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