perfect" number
Number Theory
Level
2
A "perfect" number is a number which is equal to the sum of all it's divisors. The first perfect number is 6 (3 + 2 + 1 = 6). What is the second perfect number?
The answer is 28.
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1 solution
The first perfect number is 6, because 1, 2, and 3 are its proper positive divisors, and 1 + 2 + 3 = 6. Equivalently, the number 6 is equal to half the sum of all its positive divisors: ( 1 + 2 + 3 + 6 ) / 2 = 6. The next perfect number is 28 = 1 + 2 + 4 + 7 + 14. This is followed by the perfect numbers 496 and 8128 :)