Smarandache kn数列与除数和函数的混合均值

Hybrid mean value of Smarandache kn-digital series with divisor sum function

对任意整数1≤k≤9,如果数列{a(k,n)}中的每一个数都可以分成两部分,使得第二部分是第一部分的k倍,则该数列称作Smarandache kn数字数列.利用初等及组合方法研究Smaran-dache kn数字数列及除数和函数的混合均值性质,并给出一个有趣的渐近公式.

For any positive integer k(1≤ k≤9),if the digits of {a(k,n)} can be divided into two parts,and the second part is k times of the first part,the digital series {a(k,n)} is called to Smarandache kn-digital series.The properties of the hybrid mean value of Smarandache kn-digital series with divisor sum function are studied using elementary and combinational methods,and two interesting asymptotic formulae for it are presented.