For all you math crafters out there, I have a quick question. What is the most efficient item build for raising AP as high as possible as quickly as possible?

Without regards to anything else?

I would imagine a Soulstealer, 4x ArchAngel's staff, Zhonya's Ring, but you won't have any boots. :X

Well, in regards to gold too. That's so expensive it isn't funny. o.o

There was a bug with Mejrai's Soulstealer where if you got one, got the extra 70 ap buff, and then sold it, you'd still have the extra 70 AP. If that hasn't been fixed, I would imagine you would first want to do mejrai's, than get the buff, than sell your mejrais for an Archangel's staff than work on getting as many zhonya's rings as possible.

That only works though if you are extremely good and can kill others easily enough that you have the money.
A build I use for almost any caster *and it works well* is

Mana crystal as first time
Then work on getting tears of godess *using that mana crystal*
Than work on upgrading that to a Archangles
Boots are optional in this case since you just want straight AP
After archangles, get soulstealer
then get zhonyas
if the bug still works, i would suggest selling the soulstealer after you get the full buff and getting another zhonyas.
Usually games end before I can get furthre with my build so after that I wouldn't know. Maybe more zhonyas.

this may not be the most AP effecient but it is a very reasonable way to get alot of AP.

if your trying to make a build for pure ap and trying to get the most ap possible, I'd highly suggest you stop right there. cuz getting pure ap is a bad stratagy in almost every game regardless of what hero you have. there is no hero out here who can survive with just pure AP

you need a balance between damage/health/regentive abilities so you can get pure ap to be a super glass cannon, but one power shot and your dead

Wrong, arch angels wouldn't give you the AP that you would get with other items, even with 2% more ap based on mana.

I would get a potion right away if you're looking for AP really quickly, and I'd try to keep it up I guess as it's free AP. Soulstealer right off the bat, then a rod of ages. I would then go for a Zonya ring and then after an abyssal scepter. (The -MR might not count as straight up AP, but your spells will be hitting harder so it's kind of like AP. Plus it gives you a lot of ap) then make a lich bane. I guess the last item you'd want is an arch angels. But early game you're wasting money by getting it if you dont have a huge mana pool (only a waste if you want quick and easy AP, amazing early game item for normal play tho)

I assume that you want to stack AP to do extra damage really fast. Lich bane will have you melee hard as well as giving you high ap and move speed.

you can't do both high as possible and quickly as possible.

for high as possible, it's 5x arch angel + zhonya's ring.

for quickly as possible, it's mejaj's soulstealer + 5x kage's picks.