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:

properDivs: function [x] ->
    (factors x) -- x

amicable: function [x][
    y: sum properDivs x 
    if and? x = sum properDivs y 
            x <> y 
        -> return @[x,y]
    return ø
]

amicables: []

loop 1..20000 'n [
    am: amicable n
    if am <> ø 
        -> 'amicables ++ @[sort am]
]

print unique amicables