There is a secret gathering of a group of \(n\) aliens in a very dark room. You cannot see anyone in the room, but you hear the following questions.
“Is at least one of us a Goop?"
“Is the number of Goops amongst us an even number?"
“Is the number of Goops amongst us a multiple of 3?"
\(\dots\)
“Is the number of Goops amongst us a multiple of \(n\)?"
What are all the possible values of \(n\) such that this gathering can happen? Note that each of the \(n\) aliens have asked exactly one question.