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The aliquot sum s(n) of n is the sum of the proper divisors (that is, the divisors excluding n itself, ), and equals ?₁(n) − n; the aliquot sequence of n is formed by repeatedly applying the aliquot sum function.

Example

For example, ?₀(12) is the number of the divisors of 12:

:

while ?₁(12) is the sum of all the divisors:

:

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