I'm going to push away friends.
Why would you push your friends away?
They constantly bother me asking me to go out with them.
If you're unhappy with your friends, you don't need to feel obligated to stay friends with them. However, it sounds like they are just being friendly and want to spend time with you. I don't think they are intentionally trying to annoy you.
I don't care what they mean. It's annoying.
If they mean well by their invitations but it bothers you, then you should explain that to them. It seems like they don't know that they are annoying you by asking you to come out with them. If you tell them that, I'm sure they will be understanding.