# 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.