How to plot a graphic with solution of some inequality?


I defined the function $ z(n)$ by

z[n_] := Catch[Do[i; If[Mod[Fibonacci[i], n] == 0, Throw[i]], {i, 100000}]]

and now, I would like to plot the graphic (n,z(n)) for points such that $ z(n)/n<\epsilon$ , for some given value of $ \epsilon>0$ . For instance, for $ \epsilon=0.05$ , I used the command

Catch[Do[n; If[z[n] < 0.05*n, Print[n]], {n,1, 3000}]]

which provides me many values of $ n$ , but I do not know how to make a graphic with them (they appear in some collumn). Thanks in advance.