CAJ | 학술논문

对任意的正整数n,伪Smarandache函数Z(n)定义为最小的正整数m使得n|m(m+1)/2,,即Z(n)=min{m:n|m(m+1)/2,m∈N}. 而数论函数D(n)定义为最小的正整数m使得n|d(1)d(2)d(3)…d(m),其中d(n)为Dirichlet除数函数,即D(n)=min{m:m∈N, n|∏i=1m d(i)}.利用初等方法和解析方法研究了伪Smarandache函数Z(n)与数论函数D(n)的混合函数Z(n)·ln(D(n))的均值问题,并得到一个较强的渐近公式.
대임의적정정수n,위Smarandache함수Z(n)정의위최소적정정수m사득n|m(m+1)/2,,즉Z(n)=min{m:n|m(m+1)/2,m∈N}. 이수론함수D(n)정의위최소적정정수m사득n|d(1)d(2)d(3)…d(m),기중d(n)위Dirichlet제수함수,즉D(n)=min{m:m∈N, n|∏i=1m d(i)}.이용초등방법화해석방법연구료위Smarandache함수Z(n)여수론함수D(n)적혼합함수Z(n)·ln(D(n))적균치문제,병득도일개교강적점근공식.
For any positive integer n,the Pseudo-Smarandache function Z(n)is defined as the smallest positive integer m such that n|m(m+1)/2,that is,Z(n)=min{m:n|m(m+1)/2,m∈N}. And the number theory function D (n)is defined as the smallest positive integer m such that n divide product d(1)d(2)d(3)…d(m),where d(n)is the Dirichlet divisor function,that is,D(n)=min{m:m∈N, n|∏i=1m d(i) } . The main purpose of this paper is to use the elementary method and analytic method to study the hybrid mean value problem of Z(n)· ln(D(n))invoving the Pseudo-Smarandache function Z(n)and the number theory function D(n),and to give a shaper asymptotic formula.