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    Aspiring Number

    Definition

    Let s(n) congruent σ(n) - n, where σ(n) is the divisor function and s(n) is the restricted divisor function, and define the aliquot sequence of n by s^0(n) congruent n, s^1(n) = s(n), s^2(n) = s(s(n)), .... If the sequence reaches a constant, the constant is known as a perfect number. A number that is not perfect but whose sequence becomes constant is known as an aspiring number. For example, beginning with 25 gives the sequence 25, 6, 6, 6, ..., so 25 is an aspiring number and 6 is a perfect number.