BG-MO 2018 Problem 1

Let n be an odd positive integer.Let M be a set of $n$ positive integers ,which are 2x2 different. A set $T$ $\in$ $M$ is called "good" if the product of its elements is divisible by the sum of the elements in $M$ , but is not divisible by the square of the same sum. Given that $M$ is "good",how many "good" subsets of $M$ can there be?