Bounds for Odd k-Perfect Numbers

2011/02/22 by Shi-Chao Chen, Hao Luo, Chen, Shi-Chao +1
Mathematics · #11A25 #Advanced Mathematical Theories #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Number Theory (math.NT) #math.NT #msc:11A25

paper · pdf · doi:10.48550/arxiv.1102.4397

6 pages

arxiv created 2011/02/22 · openalex publication_date 2011/02/22 · arxiv updated 2011/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k≥2 be an integer. A natural number n is called k-perfect if σ(n)=kn. For any integer r≥1 we prove that the number of odd k-perfect numbers with at most r distinct prime factors is bounded by k4^r3.

Citations

• Finiteness of the Odd Perfect and Primitive Abundant Numbers with n Distinct Prime Factors

Related

• Bounds On Factors Of Odd Perfect Numbers
• New techniques for bounds on the total number of Prime Factors of an Odd Perfect Number
• Upper bounds on the second largest prime factor of an odd perfect number
• Where do odd perfect numbers live?
• On the Sum and Product of Distinct Prime Factors of an Odd Perfect Number