For any integers x and y, we use (x,y)(［x,y］) to denote the greatest common divisor (the least common multiple) of x and y. Let f be an arithmetic function and S={x1,…,xn} be a set of n distinct positive integers.By (f(S))=(f(xi,xj))((f［S］)=(f［xi,xj］)),we denote the n×n matrix having f evaluated at (xi,xj) (［xi,xj］) as its i,j entry. The set S is called a divisor chain if there is a permutation σ of {1,2,…,n} such that xσ(1)|…|xσ(n). The set S is called two quasi coprime divisor chains if S can be partitioned as S=SI∪S2with all Si(1≤i≤2)being divisor chains and (max(S1), max(S2))=gcd(S). In this paper , we give the formulae for the determinants of the matrices (f(S)) and (f［S］) on two quasi coprime divisor chains.
