关于n进制中一个数论函数均值的计算

On Mean Value of a Number Theoretic Function in the n-nary

研究了n进制非零数字之积函数均值的计算公式问题,采用初等方法,运用猜想、归纳、递推的办法.给出积函数均值的定义,得出了Smarandache问题中n进制非零数字之积函数三次均值的精确计算公式.解决了美籍罗马尼亚数论专家F.Smarandache教授著的Only problems,not solutions一书中的部分问题,对于Smarandache问题中的积性函数理论的研究起着重要的作用.

The calculating formula about multiplication function of n-nary nonzero digital, the dement method, and the conjecture, induction as well as recursion methods were used, in this paper, the multiplication mean value definition was given, we got the third mean value formula Some questions of F. Smarandache＇s book Only problems, not solutions! have been solved, which played an important role in the research on multiplication function theory in Smarandache question.