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. 


import: mapping
 
Integer method: properDivs -- []
   #[ self swap mod 0 == ] self 2 / seq filter ;
 
: amicables
| i j |
   Array new
   20000 loop: i [
      i properDivs sum dup ->j i <= if continue then
      j properDivs sum i <> if continue then
      [ i, j ] over add
      ]
;