A pair of Positive Integers such that the equations

have a Positive Integer solution , where is the Divisor Function. If is Prime, then is an Amicable Pair (te Riele 1986). is a ``special'' breeder if

where and are Relatively Prime, . If regular amicable pairs of type with are of the form with Prime, then are special breeders (te Riele 1986).

**References**

te Riele, H. J. J. ``Computation of All the Amicable Pairs Below .'' *Math. Comput.* **47**, 361-368 and S9-S35, 1986.

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1999-05-26