关于Smarandache完全数

On the Smarandache Perfect Numbers

对于正整数a,设S(a)是a的Smarandache函数,设n是正整数.如果n满足∑d|nS(d)=n+1+S(n),则称n是一个Smarandache完全数.本文证明了:Smarandache完全数仅有n=12.

For any positive integer a, let S（a） denote the Smarandache function of a. Let n be a positive integer. If n sat-isfies ∑d｜n S（d）=n＋1＋S（n）,then n is called a Smarandache perfect number. In this paper we prove that 12 the only Smaran-dache prefect number.