How many numbers $n$ satisfy $f(n)=16$?

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The function \(f\), defined for whole positive numbers, satisfies \(f(1)=1\) and also the rules \[f(2n)=2f(n),\] \[f(2n+1)=4f(n),\] for all values of \(n\). How many numbers \(n\) satisfy \(f(n)=16\)?

1. \(3\),

2. \(4\),

3. \(5\),

4. \(6\).