Odd 'Perfect Numbers'

So called 'Perfect Numbers' have been studied and described since (at least) 300BC. They are numbers where the divisors, added together, equal the example number. e.g.

6 = 1 + 2 + 3

28 = 1 + 2 + 4 + 7 + 14

496 = 1 + 2 + 4 + 8 + 16 + 31 + 62 + 124 + 248

All 'perfect numbers' so far discovered are even. There may be odd 'perfect numbers', but despite computer searches examining 10¹⁵⁰⁰ numbers, none have been found. No proof has yet been devised to show whether they are possible or not.