Functions On The Number Of Relatively Prime Subsets

In the first chapter of this paper, we introduce the definition of the greatest common divi-sor, congruence, multiplicative function, and so on. In the second chapter, we give the proofof the formula of Euler function. In the third chapter, we introduce M.B.Nathanson’s work onfunctions counting the number of relatively prime subsets of {1,2,, n}. In the fourth chap-ter, we introduce M.Ayad and O.Kihel’s work about the generalization of M.B.Nathanson’sresult. In the fifth chapter, we give a diferent proof of the formulas of functions on thenumber of relatively prime subsets. In the sixth chapter, we draw some related conclusions.