On a dual of the Pseudo-Smarandache function

This function generalizes many particular functions. For f( k) = k! one gets the Smarandache function, while for f(k) = k(k: 1) one has the Pseudo-Smarandache function Z (see [1], [4-5]). In the above paper [3] we have defined also dual arithmetic functions as follows: Let 9 : N* -+ N* be a function having the property that for each n 2:: 1 there exists at least a k 2:: 1 such that g(k)ln. Let Gin) = max{k E N*: g(k)ln}. (2) For g(k) = k! we obtain a dual of the Smarandache function. This particular function, denoted by us as S* has been studied in the above paper. By putting g(k) = k(k: 1) one obtains a dual of the Pseudo-Smarandache function. Let us denote this function, by analogy by Z •. Our aim is to study certain elementary properties of this arithmetic function.