特殊类型奇完全数Euler因子的一些结论(英文)

Some Results of Certain Odd Perfect Numbers

奇完全数的存在性问题是一个著名的数论难题,迄今尚未解决.本文研究了特殊类型奇完全数的Euler因子,并给出了一些结论:如果n=πα32β1Q21β1是奇完全数,并且π=5时,那么α≥9;如果n=πα52β2Q22β2是奇完全数,并且π=13时,那么α≥9.

Abstract：The existence of odd perfect numbers is a well-known open problem in number theory. The Euler＇ s factors of certain odd perfect numbers were studied,and some results of theses were presented： if n = π^a3^2β1Q^21β1, is an odd perfect number and π = 5,then a≥9;if n = π^a5^2β2Q^22β2 is an odd perfect number and π = 13,then a≥9.