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. 


from proper_divisors import proper_divs
 
def amicable(rangemax=20000):
    n2divsum = {n: sum(proper_divs(n)) for n in range(1, rangemax + 1)}
    for num, divsum in n2divsum.items():
        if num < divsum and divsum <= rangemax and n2divsum[divsum] == num:
            yield num, divsum
 
if __name__ == '__main__':
    for num, divsum in amicable():
        print('Amicable pair: %i and %i With proper divisors:\n    %r\n    %r'
              % (num, divsum, sorted(proper_divs(num)), sorted(proper_divs(divsum))))