Javaconcurentprogramforthesamarandacbe Function

The aim of this article is to propose a Java concurrent program for the Smarandache fimction based on the equation sept' ..... p:.) = max{s(p~' ), ... ,S(p:·)}. Some results concerning the theoretical complexity of this program are proposed. Fmally, the experimental results of the sequential and Java programs are given in order to demonstrate the efficiency of the conament implementation. 1. INTRODUcnON In this section the results used in this article are presented briefly. These concern the Smarandache and the main methods of its computation. The Smarandache function [Smarandache, 1980] is S: N* ~ N defined by Sen) = min{k E Nlk!: n}(Vn EN *). (1) The main properties of this function are presented in the following (Va,bEN*)(a,b)= l=>S(a ·b) = max {S(a),s(b)} (2) that gives us S(p;1 ..... p:.) = max{S(p~1 ), ... ,S(P:· )}. (3) An important inequality satisfied by the function S is (Va E N *) S( a) ~ a, the equality occurring iff a is prime. (4) When the number a is not prime this inequality can be improved by (VaEN*:a notprime)S(a)~ a. 2 During the last few years, several implementation of The Smarandache function have been proposed. Ibstedt [1997, 1999] developed an algorithm based on Equation (3). The