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abundant number

A number that is smaller than the sum of its aliquot parts (proper divisors). Twelve is the smallest abundant number – the sum of its aliquot parts is 1 + 2 + 3 + 4 + 6 = 16 – followed by 18, 20, 24, and 30.

A weird number is an abundant number that is not semiperfect; in other words, n is weird if the sum of its divisors is greater than n, but n is not equal to the sum of any subset of its divisors. The first few weird numbers are 70, 836, 4030, 5830, and 7192. It isn't known if there are any odd weird numbers.

A deficient number is one that is greater than the sum of its aliquot parts. The first few deficient numbers are 1, 2, 3, 4, 5, 7, 8, and 9. Any divisor of a deficient (or perfect) number is deficient. A number that is not abundant or deficient is known as a perfect number.

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