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. 


void main() @safe /*@nogc*/ {
    import std.stdio, std.algorithm, std.range, std.typecons, std.array;
 
    immutable properDivs = (in uint n) pure nothrow @safe /*@nogc*/ =>
        iota(1, (n + 1) / 2 + 1).filter!(x => n % x == 0);
 
    enum rangeMax = 20_000;
    auto n2d = iota(1, rangeMax + 1).map!(n => properDivs(n).sum);
 
    foreach (immutable n, immutable divSum; n2d.enumerate(1))
        if (n < divSum && divSum <= rangeMax && n2d[divSum - 1] == n)
            writefln("Amicable pair: %d and %d with proper divisors:\n    %s\n    %s",
                     n, divSum, properDivs(n), properDivs(divSum));
}