"Good" subsets of natural numbers

We define a subset A of positive integers as "Good" if it's possible to write it's members as $a_1$, $a_2$, $a_3$, $\cdots$ so that GCD of any two consecutive numbers $a_i$ and $a_{i+1}$ is greater than $1$. Verify and prove "Goodness" of the following two sets:

1. Set of positive integers greater than $1$


2. Set of squares greater than $1$

How to solve this problem?