Q_3（x）的渐近公式

The Asymptotic Formula for Q_3(x)

对于自然数ｎ，用Ｇ（ｎ）表示ｎ阶群中互不同构的群的个数（同构类数），用Ｑ＿３（ｘ）表示不超过ｘ的自然数（ｎ≤ｘ）中使Ｇ（ｎ）＝３的ｎ的个数．本文的目的是用筛法证明下面渐近公式：其中ｌｏｇ＿ｒｘ＝ｌｏｇ（ｌｏｇ＿（ｒ－１）ｘ），ｌｏｇ＿１ｘ＝ｌｏｇｘ，γ是Ｅｕｌｅｒ常数．

For natural number n let G(n)denote the number of isormorphic cla-sses of groups of order n. For any number x,let Q_3(x) denote the number of value of n which are to satisfy that n≤x, G(n)= 3 and n is sqarefree simultamously.In this paper an asymptotic formula for Q_3(x)is proved by means of Brun sieve method under some assumption,that iswhere log_rX=log(log _(r-1)x),log _1x =log x,and γis the Euler constant.