Breeder

A pair of positive integers  such that the equations

(1)

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

			(2)
			(3)

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.