Flash and Exhaust is vital for Sion to initiate and take out those lucky escapes and easy ganks. Out of range with your stun is not fun. So a quick flash and the enemy's dead. Exhaust right after stun makes the target vulnerable to up to 6 seconds.

Sions AP scaling makes Cryptic Gaze and Deaths Carres a highly lethal nuke. You can easy get over 500 Ap with this build because of Archangel Staff's mana stack. Sion's stun is maxed out first because of the damage it deals and the 2 second stun. Why I don't max the shield like everyone else seem to think is best is because of it takes 3 seconds to explode at a least. If you would throw Cryptic Gaze and then pop the shield you would have 1 second left to explode it. There is no way anyone could do enough damage to destroy the shield by then.
Sions Ultimate is worthless when going with an Ap build. He has almost no damage or attack speed to make the lifesteal from the ultimate give enough health. The shield is enough protection for AP Sion.

After you've got Archangel staff, Sorcerers shoes and Zhonyas ring you can get anything else you want since this is the main build for AP Sion. Like if you need Magic penetration or resist you can get that without losing too much AP since archangel staff gives you a minor increase.

I've been two shotting people with this build almost since i started playing LoL. Stun->Death's Caress=Dead(or atleast half HP left)

Play Video
Tho this is old, it's still a reliable video to demonstrate the power of AP Sion!