On the divisibility of odd perfect numbers by a high power of a prime

2005/11/16 by Tomohiro Yamada, Yamada, Tomohiro
Mathematics · #11A25 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A25

paper · pdf · doi:10.48550/arxiv.math/0511410

13 pages

arxiv created 2007/07/31 · arxiv updated 2009/12/01

Abstract

We study some divisibility properties of multiperfect numbers. Our main result is: if N=p₁^α₁... p_s^α_s q₁^2β₁... q_t^2β_t with β₁, ..., β_t in some finite set S satisfies σ(N)=(n)/(d)N, then N has a prime factor smaller than C, where C is an effective computable constant depending only on s, n, S.

Related

• Quasiperfect numbers with the same exponent
• Odd Multiperfect Numbers
• Upper bounds on the second largest prime factor of an odd perfect number
• Bounds On Factors Of Odd Perfect Numbers
• New techniques for bounds on the total number of Prime Factors of an Odd Perfect Number