Well your W scales 100% with ap and Viego works very well with sheen which lich bane has but it doesnt do ad it does ap now, Q + AA procs Lich bane. W procs Nightharvester instantly. Those two our lethal combo. And ofc Nashor Tooth, vital if you want to-do any ap damage with AA.

It also gives you some extra MS with the E, E move speed scales 0,04% with ap. His Q passive healing also scales with AP, less than ad tho 15% ap scaling 20% ad.

This is hidden op, try it before rito fixes it. Sources, me. Go and try it now man.

Some basic combos for AP VIEGO, optimal oneshots.
One that i like that looks really clean and outputs alot of damage (Up to 2500) in less than a second.
-W + R. Really simple
You W into him stunning and applying Q passive and nightharvester, following it up with R procs both Q passive and Lichbane dealing great damage and giving you that satisfaction.
W + Q + AA
Did you know if you charge or press W, then instantly press Q after W it animation cancels the W. If you use this correct its basically A dash to Q with more damage, basically useless on regular viego but on AP viego it proccs everything on a small amount of time. W proccs NH then in with Q which basically does nothing but cancel the W animation but since your building ap, Q doesnt to damage. Then the AA will x2 the dmg.

How you fight reguarly:
You basically enter the fight with W, boom atleast half the bar is gone, follow it up with auto proccing Q passive and lichbane (massive damage). Following it up with an regular Q + AA + R AA if still alive so basically: W + AA + Q + AA + R + AA.
And it also proccs Electrocute, if you go DA it also proccs it bc of the raw damage.

Something a bit more tricky i like to do (not often) if you hold in E + W at the same time and release at the same time, you can make the E +W + AA + Q + AA + R + AA, go much quicker bc of the increased AS

You've already picked your champ, which happends to be Viego, you realize your full AD, oh no they picked Sejuani what do i do. You go ap and suprise. Your also gonna obliderate ADC's harder than AD.

Well your scaling is very slow, you need a couple of items before it starts to do alot of damage which can be frustrating if you aren't snowballing. I find this build very fun and i hope Elekktro will try it.

The major powerspikes:

When you get Recurve bow first recall makes you clear alot faster, speeds up the game.
Hextech alternator is strong early bc it doubles your W damage.

When you finally have Nashor tooth it opens up the game much more, cuz now your autos do AP. Im working on Lich Bane first item.

Lich Bane is the biggest powerspike with Rabadons in there.