There are mildewcides you can add to paint. They make them in small bottles that you mix into a gallon (just like 2-cycle mix). You can add a bottle to paint that is already mildew repellent too. I always use the stuff when painting a bathroom (as an example).
Ideally, you want to buy the stuff, and have the paint place mix it in right there using their paint shaker. It will be more evenly consistent when mixed on a shaker than when mixed with a stick or paddle.
The more surface "texture" to a paint, the more it will support mold. So semi-gloss has much less of a mold issue than flat. That's why bathrooms should never be painted in flat, but the same rule goes for exterior, as it does for interior mold.
If you already have mold and you simply power wash it off, it will quickly return. You must kill the mold. Bleach may be good for this, but there are safer chemicals for where bleach is not an option. Either way, the mold will still return, because clearly where you have mold, it is still a good habitat for mold growth, but you'll get more time between washings if you do kill the mold first.