On the total number of prime factors of an odd perfect number期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the total number of prime factors of an odd perfect number

Authors:	D. E. Iannucci R. M. Sorli.

Affiliation:	University of the Virgin Islands, St. Thomas, Virgin Islands 00802 ; Department of Mathematical Sciences, University of Technology, Sydney, Broadway, 2007, Australia

Abstract:	We say is perfect if , where denotes the sum of the positive divisors of . No odd perfect numbers are known, but it is well known that if such a number exists, it must have prime factorization of the form $n=p^{alpha}prod_{j=1}^{k}q_j^{2beta_j}$ , where , , ..., are distinct primes and . We prove that if or for all , , then . We also prove as our main result that , where $Omega(n)=alpha+2sum_{j=1}^{k}beta_j$ . This improves a result of Sayers given in 1986.

Keywords:	Odd perfect numbers factorization

	点击此处可从《Mathematics of Computation》浏览原始摘要信息
	点击此处可从《Mathematics of Computation》下载全文