sentences:  Aliquot sum
  
  In number theory, the aliquot sum "s"("n") of a positive integer "n" is the sum of all proper divisors of "n", that is, all divisors of "n" other than "n" itself.It can be used to characterize the prime numbers, perfect numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.