整数分解式的指数函数及其均值的计算

Exponential function of integer factorization and its mean value calculation

给出了整数标准分解式的数论函数β(n,p)和它的均值∑n≤Nβ(n,p)的定义,推出了整数n标准分解式的指数函数计算公式和均值∑n≤Nβ(n,p)的精确计算公式.

Let p be a prime, n be any positive integer, β(n,p) denotes the power of p in the factorization of n. In this paper, we give an exact computing formula of β(n,p) and the mean value ∑n≤Nβ(n,p).