Two integers 



N


{\displaystyle N}

 and 



M


{\displaystyle M}

 are said to be amicable pairs if 



N
≠
M


{\displaystyle N\neq M}

 and the sum of the proper divisors of 



N


{\displaystyle N}

 (




s
u
m

(

p
r
o
p
D
i
v
s

(
N
)
)


{\displaystyle \mathrm {sum} (\mathrm {propDivs} (N))}

) 



=
M


{\displaystyle =M}

 as well as 




s
u
m

(

p
r
o
p
D
i
v
s

(
M
)
)
=
N


{\displaystyle \mathrm {sum} (\mathrm {propDivs} (M))=N}

.



Example

1184 and 1210 are an amicable pair, with proper divisors:

   1, 2, 4, 8, 16, 32, 37, 74, 148, 296, 592   and 
   1, 2, 5, 10, 11, 22, 55, 110, 121, 242, 605   respectively.


Task

Calculate and show here the Amicable pairs below 20,000; (there are eight).



Related tasks
 Proper divisors
 Abundant, deficient and perfect number classifications
 Aliquot sequence classifications and its amicable classification. 


start = Now
Set nlookup = CreateObject("Scripting.Dictionary")
Set uniquepair = CreateObject("Scripting.Dictionary")
 
For i = 1 To 20000
	sum = 0
	For n = 1 To 20000
		If n < i Then
			If i Mod n = 0 Then
				sum = sum + n
			End If
		End If
	Next
	nlookup.Add i,sum
Next
 
For j = 1 To 20000
	sum = 0
	For m = 1 To 20000
		If m < j Then
			If j Mod m = 0 Then
				sum = sum + m
			End If
		End If
	Next 
	If nlookup.Exists(sum) And nlookup.Item(sum) = j And j <> sum _
		And uniquepair.Exists(sum) = False Then
			uniquepair.Add j,sum
	End If
Next
 
For Each key In uniquepair.Keys
	WScript.Echo key & ":" & uniquepair.Item(key)
Next
 
WScript.Echo "Execution Time: " & DateDiff("s",Start,Now) & " seconds"