Amicable Triple

Dickson (1913, 2005) defined an amicable triple to be a triple of three numbers such that

			(1)
			(2)
			(3)

where is the restricted divisor function (Madachy 1979). Dickson (1913, 2005) found eight sets of amicable triples with two equal numbers, and two sets with distinct numbers. The latter are (123228768, 103340640, 124015008), for which

			(4)
			(5)
			(6)

and (1945330728960, 2324196638720, 2615631953920), for which

			(7)
			(8)
			(9)
			(10)
			(11)
			(12)

A second definition (Guy 1994) defines an amicable triple as a triple such that

(13)

where is the divisor function. An example is (, , ).