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.
Further reading Wolfram Mathworld
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