数论函数值分布问题中的Erd s强度(Ⅱ)

ON THE ERDOS'S PROPERTY OF THE DISTRIBUTION OF THE VALUES OF ARITHMETICAL FUNCTIONS(Ⅱ)

考虑由Euler函数演变的密度函数φ~*(n)=φ(n)/n,证实了对于任给正整数k,存在自然数n,使得在该点函数值超过左右两邻连续k个函数值的连乘积。

For the arithmetical function φ~*(n)=φ(n)/n, here φ(n) is the Euler's function, the following result is gotten in this paper: For any given positive integer n_o and k, then there exists a natural number n, such that when n>n_o we have the so-called Erdos's property of arithmetical function. More precisely, the number of integer n satisfying(*) is infinite.