I think Malzahar. Okay, at 13000 gold, you can get Boots Rabadons Void Staff DFG Liandry's Amplifying tome Elixer
That is (120 + 120 + 70 + 50 + 20 + 74.7[runes] + 24[masteries]) = 478.7 * 1.35 = 646 AP Also, we can ignore 35% of the target's magic resist, with 41.5 additional magic penetration.
His passive will have an attack speed of 1.5, and will have an AD of 110. His Q will do 300 + 517 magic damage His W will do 8 + 6.46% Max health per second. His E will do 320 + 517 damage His R will do 550 + 840 damage
So, not factoring in Liandry's, DFG, or Magic resist, in 4 seconds, Malzahar can deal 817 + 837 + 1390 = flat 3044 magic damage, plus 65.84% of your max health Plus 328 True damage (ignite)
It is also important to note that his Q (which will be the first spell cast), has a range of 900, and will cause the victim to be silenced for 3 seconds. His ultimate will keep you under suppression for 2.5 seconds, rendering you helpless.
TL;DR, Malzahar will stomp a 1v1. --- I am on Gamefaqs using Internet Explorer for Xbox and am typing this on my Windows phone using Smartglass No, seriously, I am.