We see that 28 is still perfect by this definition: Its proper divisors are 1, 2, 4, 7 and 14, its improper divisor is 28, and the sum of all its divisors, 1 + 2 + 4 + 7 + 14 + 28, is 56, which is 2 × ...

If we do not exclude unity and the number itself when summing up divisors, the 'abundant' numbers, whose divisors' sum is greater than themselves (for example, the number 18 referred to in the ...