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Given that reloading the page is allowed, and your goal is only to prevent h from being executable more than once while it's already loaded, what's wrong with function h(){h=0}?
Certainly. In practice I'd only use a recursive function if I really needed some kind of stack, like for tree navigation or other inherently recursive data-structures. (Sure, numbers can be treated as recursive data-structures, but we have all kinds of nice abstractions to help us ignore that fact.)
Under the preexisting rules, one could say that this implementation omits the requirement "Output nothing if the inputs are relatively prime." Still seems wrong to deface golf code that came out so pretty. How brief can you make a filter() call?