United States Air Force. (Post 1947 - early 1990s)
After that the buttons changed to represent the historic "Hap Arnold" button.
Too tell you the truth it may in fact be mostly tin, or some other crappy metal to try to clean. Try a toothbrush with some household cleaners... like "simple green" or "kaboom" or something.
It's funny that these USAF buttons are not found often as they are all fairley new compared to the old brass army buttons we all love so much. I'm not sure that anyone is even interested in seriously collecting them but have seen them being sold as "unknown old military buttons" on some sites. I think thats funny because I have a closet full of them sewn to my old uniforms...
If you would like a new one to display next to this one you found I would gladly send you one and you could leave yours as it is... "as found" so to speak.
Mine are from the early 80s with a different shank type... I'd date yours based on shank type and construction as 1950s - 1960s. Maybe some older USAF members can narrow it down for you.