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Article: Mean value of F. Smarandache LCM function.(least common multiple)
- Article from:
- Scientia Magna
- Article date:
- June 1, 2007
- Author:
CopyrightCOPYRIGHT 2007 American Research Press. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
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Abstract For any positive integer n, the famous Smarandache function S(n) defined as the smallest positive integer m such that n | m!. That is, S(n) = min{m : n | m!, n [member of] N}. The Smarandache LCM function SL(n) the smallest positive integer k such that n | [1, 2,..., k], where [1, 2,..., k] denotes the least common multiple of 1, 2, ... , k. The main purpose of this paper is using the elementary methods to study the mean value properties of [(SL(n) - S(n)).sup.2], and give a sharper asymptotic formula for it.
Keywords Smarandache function, Smarandache LCM function, mean value, asymptotic formula.
[section] 1. Introduction and result
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