关于多角形数的加法补数研究

摘要

设ar(n) 是使n+ar(n)为一r角形数的最小的非负整数,即ar(n) 表示n的r角形数加法补数.运用初等方法研究了r角形数加法补数列{ar(n)}与两个数论函数Ω-(n) 和φe(n) 的复合函数Ω-(ar(n))和φe(ar(n))的均值分布,并给出了两个渐近公式.%For any positive integer n,ar(n) is the smallest nonnegative integer number such that n+ar(n) is a polygonal number,that is to say,ar(n) denotes the polygonal number additive complement.The main purpose of this paper is using the elementary method to research the mean values of Ω-(ar(n)) and φe(ar(n)),and two asymptotic formulae are obtained.