n+1 states will be needed.
When n=0 and k=1,2,3,4,5,...
L1=$2^{nk}$={ $ 2^{0}$ }={ε} , Number of states required for min DFA=1
When n=1 and k=1,2,3,4,5,...
L2=$2^{nk}$={ $ 2^{1}$,$ 2^{2}$,$ 2^{3}$,$ 2^{4}$,$ 2^{5}$,... }, Number of states required for min DFA=2
When n=2 and k=1,2,3,4,5,...
L3=$2^{nk}$={ $ 2^{2}$,$ 2^{4}$,$ 2^{6}$,$ 2^{8}$,$ 2^{10}$,... }. Number of states required for min DFA=3
L=L1 U L2 U L3 U ... U Ln
Therefore for it'll require n+1 states. Let me know if I am wrong somewhere.