On three problems concerning the Smarandache LCM sequence

Abstract

In this paper three problems posed in [1J and concerning the Smarandache LeM sequence have been analysed. Introduction In [1] the Smarandache LCM . sequence is defined as the least common mUltiple (LCM) of (1,2,3, .,. ,n) : 1,2,6, 12,60,60,420,840,2520,2520,27720,27720,360360, 360360, 360360, 720720 ...... . In the same paper the following three problems are reported: 1. If a(n) is the n-th term of the Smarandache LeM sequence, how many terms in the new sequence obtained taking a(n) + 1 are prime numbers? 2. Evaluate lim ~ a(n) where a(n) is the n-th term of the Smarandache LeM sequence n~oo~ n! n 3. Evaluate lim ~_1_ where a(n) is the n-th term of the Smarandache LeM sequence n~oo~a(n) n In this paper we analyse those three questions.