Number 20 right now is @utopian-io with 53,964M approval, or 13.59% of the total upvotes, according to steemd.com. The exact number is 53,963,817,252,985,466 on @utopian-io's account page.
According to @penguinpablo's last report (https://steemit.com/steem/@penguinpablo/weekly-report-how-much-steem-is-stored-on-the-exchanges-september-21-2018) there is 49,020,275 STEEM stored in exchanges, out of a total of 80,334,683 liquid STEEM and a STEEM supply of 277,168,974.
Now, I believe the approval weight = VESTS, and looking at the stats at SteemDB seems to bear that out, although it is confusing because they are currently two weeks out of date.. My VESTS is listed as 152,674 and my vote weight is 152,674.
So, let's assume that 53,964 M approval (ignoring all those extraneous digits) = 53,964 MVests.. We also have about 2020 VESTS = 1 STEEM, or 495 STEEM = 1 MVest. That means we need about 26,700,000 STEEM to vote somebody into the top 20. (That's at least a plausible number. It can't be 26.7 billion and it shouldn't be 26.7 thousand.)
There is currently enough STEEM in the exchanges for you to acquire that much, though at the current price of about $0.86 I don't think it's feasible (and certainly would move the market significantly.)
You might be able to lease some of the necessary SP instead of buying it.
Leased SP is 'upvoted' by the lessee, but the witness votes are still controlled by the owner. It might be feasible to construct an SP lease market where you delegate SP in exchange for proxy votes, though it would be very odd (the accounts that you would need proxies from would be accounts with high SP, and they would not need to lease much).