Problem Statement

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}

.

1184 and 1210 are an amicable pair, with proper divisors:

Calculate and show here the Amicable pairs below 20,000; (there are eight).

Let's start with the solution:

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)
      }
    }
  }
}