A note on generalized mobius (s-functions

In [1] the concept of a conjugate pair of sets of positive integers is introduced. Briefly, if Z denotés the set of positive integers and P and Q denote non-empty subsets of Z such that: if n1 (pertenece a) Z, n2 (pertenece a) Z, (n1,n2) = 1, then (1) n = n1n2 (pertenece a) P(resp. Q) n1 (pertenece a) P,n2 (pertenece a) P (resp. Q), and, if in addition, for each integer n (pertenece a) Z there is a unique factorization of the form (2) n = ab , a (pertenece a) P, b (pertenece a) Q, we say that each of the sets P and Q is a direct factor set of Z, and that (P,Q) is a conjugate pair. It is clear that P (intersección) Q = {11}. Among the generalized functions studied in [1]