random maths thought: a perfect number is the sum of all its proper divisors. A tri-perfect number has its proper divisors add to twice the number (which is three times the number if you include the number itself as one of its divisors, hence "tri-".) There are 4-perfect numbers, 5-perfect, etc. I thought: is there a 0-perfect? Obviously not: divisors+self can't equal self. But a "half-perfect" number: divisors add to half the number? 2 is one (the only one?) but I can't think of a proof why.
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