# You wish they were multiplied

$\displaystyle f(n+2)=\frac { f(n+1)+f(n) }{ \gcd(f(n),f(n+1)) }$

A function $$f : \mathbb{N} \to \mathbb{N}$$ satisfies the above equation for all $$n \in \mathbb{N}$$ and it has an upper bound. Find the sum of all possible values of $$f(2016)$$.

Clarification: $$\mathbb{N}$$ denotes the set of positive integers $$\{1, 2, 3, \ldots\}$$.

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