Let s(n) congruent σ(n) - n, where σ(n) is the divisor function and s(n) is the restricted divisor function. Then the sequence of numbers s^0(n) congruent n, s^1(n) = s(n), s^2(n) = s(s(n)), ... is called an aliquot sequence. If the sequence for a given n is bounded, it either ends at s(1) = 0 or becomes periodic. 1. If the sequence is a constant, the constant is known as a perfect number. A number that is not perfect, but for which the sequence becomes constant, is known as an aspiring number. 2. If the sequence reaches an alternating pair, it is called an amicable pair.
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