I take 21/0/9 (like most AP mages with mana
3 in brute force, helps last hitting, auto attack harass, more dmg than 3 AP
4% CDR who doesnt like?
10% Magic Pen 50% with void staff
Blast:18 AP, kinda iffy, but its the only way to get Archmage
Archmage 5% more AP 35% WITH DEATHCAP
Executioner 6% dmg, not a lot but its starts activation at 40% it WILL add up
Max mana: useful laning
Meditation: mana regen, spam spells without worry!
Runic affinity: 20% MORE TIME ON BUFFS? 20% MORE TIME FOR MORE SPAM AND DAMAGE

I'm really still testing this out, but its been pretty decent in terms of mana and AP.
Yes:
Rylais
Deathcap
Athenes
Void staff
Abyssal scepter
deathfiregrasp
morellos evil tome
Zhonyas hourglass

No w/ explanation
Rod of Ages: Ahri needs damage, Catalyst gives you none, max mana is useless on ahri if you use your spells carefully. AP why not? but it only gives 60 at the beginning, rylais also includes a slow, and who doesnt want a slow?

Lich Bane
Ok, this item is really THAT bad, but that mana wont be used much, 7% speed isnt a lot, and ahri doesnt auto attack much anyways.


Ok items w/ explanation
Will of the Ancients: I rarely get this on ahri, i find the aura useless and 20% spell vamp wont help much in teamfights. Your still ganna get focused bub.

Archangles's Staff
If your planning on late game, this would be useful with Rod of Ages and Lich Bane, however, you will have NO CDR, your early game will do no damage, and your quite easy to kill. On the
up side, mana regen, max mana, and AP. who doesnt like?

Pro
High AP (damage)
good passive, helps stay in lane
charm so OP....
SO FAST
has nine tails

Cons
Squishy (like all mages)
Skill shots (good or bad)
ult doesnt get shorter CD if you only use it once...
Needs $$ to do well