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. 


10 LET limit=20000
20 PRINT "Amicable pairs < ";limit
30 FOR n=1 TO limit
40 LET num=n: GO SUB 1000
50 LET m=num
60 GO SUB 1000
70 IF n=num AND n<m THEN PRINT n;" ";m
80 NEXT n
90 STOP 
1000 REM sumprop
1010 IF num<2 THEN LET num=0: RETURN 
1020 LET sum=1
1030 LET root=SQR num
1040 FOR i=2 TO root-.01
1050 IF num/i=INT (num/i) THEN LET sum=sum+i+num/i
1060 NEXT i
1070 IF num/root=INT (num/root) THEN LET sum=sum+root
1080 LET num=sum
1090 RETURN