关于F.Smarandache的一个问题

On a problem of F.Smarandache

设 n是一个正整数 ,a(n)表示 n的平方补数 ,即 a(n)表示使 nk为一完全平方数的最小正整数 k。本文的主要目的是研究 a(n)的均值性质 。

Let n be a postive integer, a(n) is a square complements of n, that is ,a(n) is the smallest integer k such that nk is a perfeet square. The main purpose of this paper is to study the mean value property of a(n), and use the elementary methods to give two interesting asymptotic formulas.