Using analytic methods the mean value of divisor function in the square-free number are studied,and a perfect asymptotic formula of this function is obtained.
利用解析的方法研究了除数函数d(n)在square-free数中的均值问题,并得到了关于这个函数的一个完美的渐近公式。
The study of divisor and divisor function d(n) are the most basic and important in number theory.
若一个整数m可表示为正整数n与它的除数函数d(n)之商,则称m为优美指数。
It is proved that there exist infinitely many positive integers n satisfying δ(n)/n>(d(a0)+d(a1)+…+d(ak))/(k+1),where ai(i=0,1,…,k) are all digits of the decimal notation of n,and d(ai)(i=0,1,…,k) is the divisor function of ai.
证明了:存在无穷多个正整数n,可使δ(n)/n>(d(a0)+d(a1)+…+d(ak))/(k+1),其中ai(i=0,1,…,k)是n的十进制表示中的所有数位上的数字,d(ai)(i=0,1,…,k)是ai的除数函数。