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. 


let isqrt = (v) => {
  Belt.Float.toInt(
    sqrt(Belt.Int.toFloat(v)))
}
 
let sum_divs = (n) => {
  let sum = ref(1)
  for d in 2 to isqrt(n) {
    if mod(n, d) == 0 {
      sum.contents = sum.contents + (n / d + d)
    }
  }
  sum.contents
}
 
{
  for n in 2 to 20000 {
    let m = sum_divs(n)
    if (m > n) {
      if sum_divs(m) == n {
        Printf.printf("%d %d\n", n, m)
      }
    }
  }
}
 