最大k次因子的估计

Estimates of Maximal Divisor of k-th Power

令δk(n)=max{d:dk|n},0<v<k．本文研究了和式Tk,v(x,y):= ∑x<n≤x+yδkv(n),并对合适小的y,给出了Tk,v(x,y)的渐近公式,改进了前人的结果．

In this paper, we study the sum Tk,v（x,y）：=∑x〈n≤n＋yδk^v（n）,where δk（n）=max{d：d^k｜n},0〈v〈kFor suitably small y, the asymptotic formula of Tk,v,（x, y）is built, which improves the previous result.