素因子函数Ω(n)的二次均值

The Second Power Mean Value of the Prime Factor Function Ω(n)

设Ω(n)表示正整数n的全部素因子的个数,即若n=p1α1p2α2…prαr,其中pi(1≤i≤r)是不同的素数,则Ω(n)=α1+α2+…+αr.文章主要利用初等方法探讨Ω(n)的二次均值,并给出∑n≤xΩ2(x)的渐近公式.

Let ll（n） counts all the numbers of prime divisors of the positive integer n, that is,n=PlαlP2α2…pr^αr , Pi Pi（1≤i≤r）are distinct primes, then Ω（n）=α＋α2＋…＋α, The main purpose of this paper is to study the second power mean value of the prime factor function Ω（n） by using elementary methods, and an asymptotic formula is given.