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. 


Chasing Chains of Sums of Factors of Numbers.
Perfect!! 6,
Perfect!! 28,
Amicable! 220,284,
Perfect!! 496,
Amicable! 1184,1210,
Amicable! 2620,2924,
Amicable! 5020,5564,
Amicable! 6232,6368,
Perfect!! 8128,
Amicable! 10744,10856,
Amicable! 12285,14595,
Sociable: 12496,14288,15472,14536,14264,
Sociable: 14316,19116,31704,47616,83328,177792,295488,629072,589786,294896,358336,418904,366556,274924,275444,243760,376736,381028,285778,152990,122410,97946,48976,45946,22976,22744,19916,17716,
Amicable! 17296,18416,
