Using defn or fn it\'s easy to create a function that taking one argument that ignores it and returns 1:
(defn ret1 [arg] 1)
(fn [arg] 1)
Is it
The #() syntax can't be used to create functions that have unused parameters in the way your description requires. This is a limitation of the #() reader macro.
I would recommend not using #() and instead just writing (constantly 1) which is a very brief way to create a function that ignores a parameter and instead always returns 1.