A number theory problem by Ilham Saiful Fauzi

Let \(d(n)\) is the greatest odd divisor of \(n\). We define a function \(f\) such that: \(f(2n-1)=2^{n}\) and \(f(2n)=n+\dfrac{2n}{d(n)}\). Find the number of composition \(k\) such that \(f^{k}(1)=2016\)

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