Any pointers on this troublesome algorithm?

[Cryo]

After working on this off and on for quite a while, I can't seem to really find any way to crack this. However, one thing I have noticed is that each of the generated ciphertext all have a GCD of 9. Is it a common expectation of RSA-generated ciphertexts to have a similar GCD, or does the fact that they all have a GCD > 1 mean that the possibilities can be reduced by any amount?

Thanks again for the helpful advice! I've been studying crypto more, but couldn't quite find whether this situation was expected or whether it indicated a vulnerability in this particular implementation.