20/04/2010

ALIQUOT SEQUENCES

aliquot.jpgAn aliquot sequence is a recursive sequence in which each term is the sum of the proper divisors of the previous term.
There are 5 cases:
1) The sequence ends with 1.
2) The sequence ends with the starting number and then repeats (Sociable Numbers).
3) The sequence is made by only two numbers (Amicable Numbers).
4) The sequence is made by only one number (Perfect Number).
5) Some numbers have an aliquot sequence which is eventually periodic, but the number itself is not perfect, amicable, or sociable (ex. 95).

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