特殊类型奇完全数Euler因子的一些结论

摘要

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=π^a3^2β1Q^21β1 ,是奇完全数，并且π=5时，那么a≥9；如果n=π^a5^2β2Q^22β2是奇完全数，并且丌=13时，那么a≥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.