关于偶完全数和n-完全数（英文）

On the even perfect numbers and n-perfect numbers

对于任意的正整数a,设δ(a)表示a的所有除数之和.如果δ(x)=2x,则正整数x称作完全数.设n是一个给定的正整数.如果δ(y)+δ(ny)=2(n+1)y,则n称作n-完全数.为了得到偶完全数和n-完全数之间的关系,本文利用δ(a)的性质,证明了如果x是偶完全数,y是x-完全数,那么有(x,y)=(6,13).

For any positive integer a,letδ（a）denotes the sum of all divisors of a.A positive integer xis called a perfect number ifδ（x）=2x.Let n be a fixed positive integer.A positive integer yis called an n-perfect number ifδ（y）＋δ（ny）=2（n＋1）y.In order to give a relation between even perfect numbers and n-perfect numbers,by using certain properties ofδ（a）,it is proved that if xis an even perfect number and yis an x-perfect number,then we have only（x,y）=（6,13）.