For any real number x,[x]denotes the integer part of x.F_(1),F_(2) denote two multiplicative function classes which are small in numerical sense.In this paper,we study the summation∑_(n≤x)f([x/n])for f∈F_(1).As spe...For any real number x,[x]denotes the integer part of x.F_(1),F_(2) denote two multiplicative function classes which are small in numerical sense.In this paper,we study the summation∑_(n≤x)f([x/n])for f∈F_(1).As specific cases,we take d^((e))(n),β(n),a(n),μ_(2)(n)denoting the number of exponential divisors of n,the number of square-full divisors of n,the number of non-isomorphic Abelian groups of order n,and the characteristic function of the square-free integers,respectively.In the case ofμ_(2)(n),we improved the result of Liu,Wu and Yang.The sums shaped likeΣ_(n≤x)f([x/n]+f([x/n]))for f∈F_(2) are also researched.展开更多
基金Supported by the National Natural Science Foundation of China(Grant No.11971476)。
文摘For any real number x,[x]denotes the integer part of x.F_(1),F_(2) denote two multiplicative function classes which are small in numerical sense.In this paper,we study the summation∑_(n≤x)f([x/n])for f∈F_(1).As specific cases,we take d^((e))(n),β(n),a(n),μ_(2)(n)denoting the number of exponential divisors of n,the number of square-full divisors of n,the number of non-isomorphic Abelian groups of order n,and the characteristic function of the square-free integers,respectively.In the case ofμ_(2)(n),we improved the result of Liu,Wu and Yang.The sums shaped likeΣ_(n≤x)f([x/n]+f([x/n]))for f∈F_(2) are also researched.
