关于k重S-完全数

On the k Fold S-Perfect Numbers

对于正整数n,设S(n)是Smarandache函数,f(n)=∑d|nS(d).对于正整数k,若n适合f(n)=kn,则称n是一个k重S-完全数.证明了:当k>2时,不存在k重S-完全数.

For any positive integer n, let S （n） denote the Smarandache function of n. Further let f（ n ） =∑dln S（d）. For a fixed positive integer k, if n satisfies f（ n ） = kn, then n is called a k fold S-perfect number. It is proved that if κ 〉 2, then there is no k fold S-prefect number.