Anodizing is the best possible surface for paint adhesion. No special primers or anything like that normally associated with painting aluminum is required. Bare aluminum is highly reactive with air. It doesn't matter what you do to get the surface bare, chemically or mechanically, because it immediately begins to reform oxide to protect itself. An anodized surface is non-reactive, or inert, in atmospheric exposure. That's why its appearance stays substantially the same over time. Because it is inert there's no need to apply any chemical or primer whose purpose is to convert the surface from reactive to inert. Also, the method of "growth" of the anodized surface leaves it somewhat porous on a microscopic basis, so it has ideal properties for letting the paint "grip" the surface. As an example of how well anodized aluminum holds paint, all pre-painted architectural sheet aluminum is first anodized and then painted with no primer of any kind between the surface and the topcoat. You can typically take a piece of this painted sheet, bend it in a brake, and fold it flat on itself like a hemmed edge, and the paint will remain intact.
Try a piece and see for yourself. The same paint that will almost peel off bare aluminum in sheets will have to be blasted or sanded off an anodized surface.