一类数论函数均值的误差项

The Error Term for a Kind of Number Theoretic Functions

设n为任意的正整数 ,σ(n)为n的除数和函数 ,E(x)表示和式 ∑n≤xσ(n)n 渐近公式中的误差项。研究了E(x)的性质 ,给出 ∑n≤xE(n)和∫x1E(t)

Let n be a positive integer,σ(n) be the divisor sum function of n. E(x) denotes the error term in the asymptotic formula for ∑n≤xσ(n)n.The main purpose of this paper is to study the properties of E(x),and give two interesting asymptotic formulas for ∑n≤xE(n) and ∫ x 1E(t)dt.