An equation involving the functions Z(n) and D(n) and its all positive integer solutions

For any positive integer n, the famous pseudo Smarandache function Z(n) is defined as the smallest positive integer m such that n | m(m+1)/2. The number theory function D(n) is defined as the smallest positive integer m such that n divides d(1)d(2)…d(m), where d(n) is the Dirichlet divisor function. The main purpose of this paper is using the elementary method and the properties of the pseudo Smarandache function Z(n) and number theory function D(n) to study the solvability of the equation 2Z(n) = D(n), and obtain its all positive integer solutions.