摘要
对任意正整数n,Smarandache最小平方数列SP(n)定义为大于或等于n的最小完全平方数;而Smarandache最大平方数列IP(n)定义为小于或等于n的最大完全平方数.日本学者建议研究数列SP(n)和IP(n)的几个均值问题.最近,国内学者首次利用初等及解析方法对这些问题进行了研究,并给出了数列SP(n)及IP(n)的几个均值公式,同时解决了日本学者提出的几个问题.本文进一步对这些问题进行研究,获得了一个新的渐近公式.
For any positive integer n, the Smarandache Superior Square Part SP（n） is the smallest square greater than or equal to n, the Smarandache Inferior Square Part IP（n） is the largest square less than or equal to n. Japanese scholar asked us to study several mean value problems related to sequences SP（n） and IP（n）. Recently, Chinese scholar first used the elementary and analytic methods to study these problems, obtained several interesting mean value formulae, and solved several problems proposed by Japanese scholar. The main purpose of this paper is also to study the properties of the Smarandache square parts sequences, and give a new asymptotic formula involving SP（n） and IP（n）.
出处
《纯粹数学与应用数学》
CSCD
2010年第1期69-72,共4页
Pure and Applied Mathematics
基金
国家自然科学基金(10671155)
