Odd amicable pair

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This may be a bit of an uneducated guess or question but are there two numbers which are perfect squares, odd and amicable?

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No. If a number is a square, then its sum of divisors is odd. Now if the number itself is odd, that makes the sum of its proper divisors even. So if one number in an amicable pair is an odd square, the other must be even.

AFAIK, no such pairs are known, but that's another story.