# Aliquot sum

In mathematics, the **aliquot sum** *s*(*n*) of a positive integer *n* is the sum of all proper divisors of *n*. The aliquot sums of perfect, deficient, and abundant numbers are equal to, less than, and greater than the number itself respectively. The aliquot sequence is the sequence obtained by repeatedly applying the aliquot sum function *s*. The aliquot sum function is also referred to as the restricted divisor function.^{[1]}

For example, the proper divisors of 15 (that is, the positive divisors of 15 that are not equal to 15) are 1, 3 and 5, so the aliquot sum of 15 is 9 (1 + 3 + 5).

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