有关次幂原数函数的若干性质

摘要

Let p be a fixed prime, for any positive integer n, the primitive function of power p is defined as the smallest positive integer m such that pn|m!. That is , Sp(n)=min{m:pn|m!}, where p is a prime. Some properties of Sp(n) is studied by using elementary methods, and two conclusions of S pk-1(SP (nk)+p sp(nk)p2! ",n=q pk-1p-1 -K+1+[ qp ]+[ qp2 ]+…are obtained.%押对于任意给定的正整数n,p次幂原数函数Sp（n）表示使pn|m！的最小正整数m,即Sp（n）=min{m：pn|m！}，其中p为素数。对给定的正整数k，用初等方法研究了函数Sp（nk）与Sp（n）之间的关系，以及Sp（n）的值与项数n的对应关系，得到了SkP (n)=pk-1 SP （nk）+p sp(nk)p2！"#$,n=q pk-1p-1-k+1+[ qp ]+[ qp2]+…。