READ THE EXPLANATION BEFORE YOU VOTE DOWN
Now before you scoff at the idea of AP Nasus, let me say first off that it is not for everyone, but for those of you who like to one "2 Q" inhibitors then maybe you would be interested in what this build offers. The reason you would build Nasus Ap is because of the fact the Lich Bane converts all of your ability power into physical damage, while the Ap will scale with your ultimate and spirit fire well. Because Ap items always add more AP than AD items add AD, you will gain more damage earlier while still being able to remain slightly tanky. Ap Nasus is very situational so i will offer a few different options for you to try. Remember, any build is not law, definitely do not follow it blindly.

You want to pick flat armor seals for early game advantage in solo lane but you can always switch up armor for mana/5. I also chose to do Ability power/LVL glyphs because late game it will be adding around 30AP from the runes alone + 35% bonus from death cap and masteries. thats a significant bonus! but i feel that adding tanky runes helps Nasus play very similarly to traditional builds. Most importantly are the Armor penetration marks and quints, they are your bread and butter for early game kills.

for masteries, i have had success with 24-5-1 for its sheer damage output in the offensive masteries, as well as adding a little more tankiness early game with 5 points in defense. With the summoner Spells i recommend you want the one point in utility for the bonuses on the spells. Your promoted minion is specifically good with the point in utility as it receives an armor bonus and will be more effective against turrets which is a must.

The items i have listed are just my usual core for Ap Nasus, i know sheen is pushed back a little bit more than people like with nasus but i feel that it is helpful to get Phil Stone and Heart of Gold not only for the Gold per second but the regen's and health bonus while solo lane. after sheen and merc treads you want to rush robadon's, it does not make sense to get litch bane before Robadon's because the damage turns out to be about the same and you lose the AP scale that you would get on your other abilities with Robadons first. All of this ends up being a fairly quick build with the gold per five. Just do what Nasus does best and q farm like a boss.

HERE IS THE IMPORTANT PART

If you are running into strong tanky champions, get last whipser immediately after lich bane. If you have sufficient Q farm you should be doing around 800 base damage with your q at 25 min before last whisper.

If you are Dominating already, just go for an Hourglass for the extra armor and 100 more damage per attack plus your ulti should be doing aroun 8% of their health in magic damage, assuming it isn't maxing out on them already.

Another good idea is getting Ryla's Crystal Scepter for the slow when you ulti or cast Spirit fire, they won't be able to escape your QQ. plus the Armor reduction on spirit fire will make it rain body parts from the squishy carries.

Remember, these are only suggestions and will not always be right for the situation. always check to see who is most fed/farmed on their team and build accordingly

Skills Sequencing is best with maxing Q first for early damage and helping with your Q farm. i take a point in wither by lvl 4. if your jungle wants to gank lvl 2 be sure to communicate that and get wither at lvl 2 instead of spirit fire. i like to max spirit fire second because it can help turn the tide in a team fight over and area, while wither is only effective on one target. One point in wither is always sufficient to secure a kill, plus it keeps in mana cost down.

I like to Pick teleport and promote for solo top because of a few reasons:
Promote
1. Promote can be used to push the lane back against a strong pusher while still giving you the gold

2. Once you kill your opponent with your OP QQ you can easily deal significant damage to their tower with promote, or even kill it with a single push.

Teleport
1. Teleport allows for a quick return to your lane allowing for minimal xp loss and maximum farm while you go back to get your gold per five items.

2. You can teleport to change the tide of any team/lane fight with Nasus, this allows you to continuously farm your Q while still being able to be and effective teammate. With Nasus' very powerful abilities you will ensure an early feed for your team.
Remember you can teleport to ward, Shaco boxes, Teemo shrooms, tell your teammate to run to one of those while you teleport in and save the day

With this build you will be dishing out significant damage the more AP you build. all the AP is going to strengthen your abilities as well as add significant damage to your Q. You still become the overlord of the team fight when you walk in, you will still be able to initiate but do not get out of position. It is best to wait until the other team has dedicated themselves to the fight so you can deal the most damage with your ultimate and AOE. always focus the carries with nasus with wither and q, you will be able to easily kill them.

Pro's
Scale the effectiveness of your abilities
Mid-Late game damage is VERY high
Kills Turrets and Inhibitors VERY quickly

Con's
Not as Tanky As traditional builds
a lot is expected of players who play nasus.
Early game is difficult without support/must play reserved