If N denotes the set of all positive integers and if $f: N \to N$ is defined by $f(n) =$ the sum of positive divisors of n then, $f(2^k.3),$ where k is a positive integers, is :

Question

$$\begin {array} {1 1} (a)\;2^{k+1} -1 & \quad (b)\;2(2^{k+1}-1) \\ (c)\;3(2^{k+1}-1) & \quad (d)\;4(2^{k+1}-1) \end {array}$$