Upper bounds on the second largest prime factor of an odd perfect number

2018/12/19 by Joshua Zelinsky · 1 citation
Mathematics · #Analytic Number Theory Research #Limits and Structures in Graph Theory #History and Theory of Mathematics

paper · doi:10.1142/s1793042119500659

openalex publication_date 2018/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Acquaah and Konyagin showed that if [Formula: see text] is an odd perfect number with prime factorization [Formula: see text], where [Formula: see text], then one must have [Formula: see text]. Using methods similar to theirs, we show that [Formula: see text] and that [Formula: see text] We also show that if [Formula: see text] and [Formula: see text] are close to each other, then these bounds can be further strengthened.

Citations

• The second largest prime divisor of an odd perfect number exceeds ten thousand
• On the number of prime factors of an odd perfect number
• ON PRIME FACTORS OF ODD PERFECT NUMBERS
• An improvement of an inequality of Ochem and Rao concerning odd perfect numbers

Cited by

• Perfect number [wikipedia]

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• Bounds On Factors Of Odd Perfect Numbers
• On the Sum and Product of Distinct Prime Factors of an Odd Perfect Number
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