一类奇完全数的倒数和的一个注记(英文)

A note on the sum of series of a class of odd perfect numbers

奇完全数的存在性问题是一个著名的数论难题,迄今远未解决.在奇完全数存在的条件下,研究了一类奇完全数n的倒数所组成的级数,得到结论:∑1/n<7.6937609×10(-179),其中(3,n)=(5,n)=1,n包括所有的奇完全数。

The existence of odd perfect numbers is a well-known open problem in number theory. On the supposition that odd perfect numbers do exist, a conclusion that ∑ n 1/n〈7.6937609×10 -179 is given roughly, where n is an odd perfect number, and n includes all odd perfect numbers, （3,n） = （5,n） = 1.