具有五个相异素因子的某些奇正整数的刻画

Characterizations on certain odd positive integer with five distinct prime factors

设N是正整数,若σ(N)=2N-d,则N被称为亏度为d的亏完全数,其中d为N的正真因子,σ(N)表示N的所有正因子的和函数。利用初等方法,讨论了具有五个相异素因子的奇亏完全数的存在性问题,给出了具有五个相异素因子的奇正整数不是奇亏完全数的一些结论。

Let N be a positive integer.Ifσ(N)=2N-d,then N is called a deficient-perfect number with deficient factors d,where d is a positive proper factor of N,andσ(N)denotes the sum of all positive factors of N.By using elementary method,the existence of odd deficient-perfect numbers with five different prime factors is discussed,and some conclusionsare made that odd positive integer with five different prime factors is not odd deficient-perfect numbers.