top 20 is hard to get in w/o strong reference letters and related research experience...
i think you should aim for schools w/ a ranking around 50 and it has to match your interest....
by aiming for, i meant the so-called "match" schools... you could apply top ones, but honestly i dont think you have a good shot...
and one more piece of advice, pure math is a broad term, you'd better figure it out which specific area you want to focus on.... i think pure math can be different from pure math, like algebra and analysis...