与三个数论函数有关的一类复合方程的可解性

Solvability of a Class of Composite Equations Related to Three Numbertheory Functions

利用初等和解析的方法与技巧,研究了一类包含了伪Smarandache函数Z(n)、简数根函数与p次幂原数函数Sp(n)的复合数论函数方程的可解性,分别得到了每个方程的全部解,并推广了一个关于计算p次幂原数函数Sp(n)值在n>p时,更加简易的计算公式以及证明该公式所用的方法.

By using the methods and techniques of elementary sum analysis,a class of functions containing pseudo-Smarandache functions Z(n), simple number root function and the primitive numbers of power p function S p(n) is studied.The whole solution of each equation is obtained respectively.The primitive numbers of power p function S p(n) values were presented by a simpler calculation formula when n>p .