设n为正整数,F.SmarandacheLCM函数SL(n)和函数SM(n)定义为:SL(1)=1,SM(1)=1,当n＞1,并且n的标准分解式为n =Pα11Pα22…Pαkk时,SL(n)=max{Pαii,SM(n)=max1≤i≤k{αi· Pi},利用初等方法及素数的分布性质研究函数(SL(n)-SM(n))2的均值性质,并给出了一个有趣的渐近公式.%Let n be a positive integer,Smarandache LCM function and Smarandache function SM(n) are defined as follows:SL(1) =1,SM(1) =1,SL(n) =max {Pαii} and SM(n) =max1≤i≤k { αi · Pi } when n ＞ 1 and n can be factorized as n =Pα11 Pα22 …Pαkk· A hybrid mean value problem of the function (SL(n)-SM(n)) 2 is studied and an interesting asymptotic formula is given by using the elementary method and the distribution property of prime numbers.
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