I have found that generally, planting anything at the base of corn interferes with hilling and fertilizing. Its much easier if you can just pull up soil to hill, and hoe to weed and side dress.
For that reason, I prefer to plant my legume crop BEFORE (previous to) corn. So far my favorites are peas and fava beans. I plant them in double rows with wide enough spacing so that a double row of corn can be planted in between the legume rows when they are producing or just about ready to start harvesting. Ideally corn is ready to be hilled when the legumes are finished.
Something short season could be sown after corn has been hilled. I've tried bush beans and that works. I think peanuts would be too long season. Corn would be done way before, and the peanuts may prevent or interfere with clean up. Plus, in removing the stalks, even if you were to just cut them close to the base, you could accidentally damage the fragile peanut plants. I also think the bulky and octopus/stilt-like aerial roots of the corn could even block peanuts from burrowing properly ...they take up a wide area. I agree, too, that the corn might cast too much shadow.
Pole beans are better used with flour or popcorn that will take full season to mature. The corn also need to be sturdy tall variety. I've tried squash under the corn -- vigorous varieties will try to climb the corn. In either case, in my tiny patches of corn, anything climbing the corn can block proper pollination.
A companion crop I'd like to try with corn is one of the mushrooms that can grow in wood chip or straw mulch.
...heh... I think I started to ramble -- I hope I was clear enough.
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