无k重次方因子的乘法分拆的个数  

On the Number of Multiplicative Partitions with K-Free Factors

作　　者：王文静 戴浩波 WANG Wenjing;DAI Haobo(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《牡丹江师范学院学报（自然科学版）》2022年第2期1-5,共5页Journal of Mudanjiang Normal University：Natural Sciences Edition

基　　金：国家自然科学基金项目(11501007)。

摘　　要：设f_(k)(n)为把n分解成无k重次方因子的乘法分拆的个数,不考虑因子顺序,利用Dirichlet级数等一系列算法得到f_(k)(n)的均值为∑_(n≤x) f_(k)(n)~c1xe(2/logx/ζ(k))4π^(1/2) (logx)^(3/4)ζ(k)^(1/4),其中,ζ(k)=∑∞n-1n^(k).Let f_(k)(n)denote the number of multiplicative partitions of n into k-free factors,where the order of the factors does not count.This paper mainly uses a series of algorithms such as Dirichlet series and conclusion the average of f_(k)(n)is∑n≤xf_(k)(n)~c1xe(2/logx/ζ(k))4π^(1/2) (logx)^(3/4)ζ(k)^(1/4),whereζ(k)=∑∞n-1n^(k).

关 键 词：分拆函数 均值 Euler乘积 DIRICHLET级数 

分 类 号：O156.4[理学—数学]