In mathematics, a
perfect number is defined as a
positive integer which is the sum of its proper positive
divisors, that is, the sum of the positive divisors not including the number itself. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors, or
σ(
n) = 2
n.
The first perfect number is
6, because 1, 2, and 3 are its proper positive divisors and 1 + 2 + 3 = 6. The next perfect number is
28 = 1 + 2 + 4 + 7 + 14. The next perfect numbers are
496 and
8128
These first four perfect numbers were the only ones known to early
Greek mathematics.
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