Cubes of Perfection
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|Ivars Peterson (MathTrek)|
|...Six is the smallest perfect number. Twenty-eight comes next. Its proper divisors are 1, 2, 4, 7, and 14, and the sum of those divisors is 28. Incidentally, if the sum works out to be less than the number itself, the number is said to be defective (or deficient). If the sum is greater, the number is said to be abundant. There are far more defective and abundant numbers than perfect numbers. However, do abundant numbers actually outnumber defective numbers? I'm not sure... the largest known perfect number, which has 1,819,050 digits, is the sum of the cubes of the first 2^1,510,688 consecutive odd integers.|
|Levels:||Middle School (6-8), High School (9-12), College|
|Math Topics:||Number Sense/About Numbers, Prime Numbers, Sequences and Sets|
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