有关次幂原数函数的若干性质

Some Properties of Primitive Function of Power

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-1/p-1-k+1+[q/p]+[q/p2]+…。

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 k a prime. Some properties of Sp（n） is studied by using elementary methods, and two conclusions of Spk（n）=pk-1（Sp（nk）＋p{sp（nk）/p2}）,n=qpk-1/p-1-k＋[q/p]＋[q/p2]＋….