关于伪Smarandache函数的一个下界估计

A lower bound estimate for the Pseudo-Smarandache function

利用初等方法及组合方法研究了伪Smarandache函数在2p+1与2p-1上的下界估计问题;给出了伪Smarandache函数在这些特殊值上的较强的下界估计;并证明了估计式Z(2p+1)≥10p,Z(2p-1)≥10p,其中p≥17为任意的素数.

Using the elementary method to study a lower bound estimate problem of the Pseudo Smarandache function at some special values .It is proved the estimates Z（2^p＋1）≥10 p ,Z （2^p -1）≥10p ,where p≥17 is any prime .The sharper lower bounds of the PseudoSmarandache function is given .