If a number’s proper divisors add up to the number itself, we call the number Perfect. Example: 6 is perfect, since its proper divisors are 1, 2, & 3 and 1 + 2 + 3 = 6.
If a number’s proper divisors add up to less than the number, we call the number Deficient. Example: The proper divisors of 9 are 1 & 3. Since 1 + 3 adds to less than 9, we call 9 Deficient.
If a number’s proper divisors add up to more than the number, we call the number Abundant. Example: The proper divisors of 12 are 1,2,3,4, & 6. Since they add up to 16, which is more than 12, we call 12 Abundant.