Which phrasal verbs or verbs can be used when mentioned visiting a website on the Internet?
For example, I would like to say
I have not visited this website for months.
Can I say
I haven't got on this website for months.
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One view of the Internet treats websites like any other physical location:
I haven't visited this website in a while
I haven't been to this website in a while
I haven't gone to this website in a while
Another view treats websites like documents, bulletin boards, or archives:
I haven't viewed this website in a while
I haven't opened this website in a while
I haven't checked this website in a while
I haven't caught up on this website in a while.
You can use "got on" but usually for sites that require some kind of authentication (like a username/password) to access your account:
I can't get on the company website. It says my password is expired.
Can you get on Facebook? I posted all the pictures of us there.
Your second example sounds unnatural and instead implies that you haven't visited the website because you were not able to connect to the website, not for lack of trying (for example, if the website had been offline for months).
I would suggest either:
I've not viewed this website for months.
I've not been to this website for months.
Or, for a website for which you have an account, perhaps:
I've not logged into this website for months.