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. 


using Primes, Printf
 
function pcontrib(p::Int64, a::Int64)
    n = one(p)
    pcon = one(p)
    for i in 1:a
        n *= p
        pcon += n
    end
    return pcon
end
 
function divisorsum(n::Int64)
    dsum = one(n)
    for (p, a) in factor(n)
        dsum *= pcontrib(p, a)
    end
    dsum -= n
end
 
function amicables(L = 2*10^7)
    acnt = 0
    println("Amicable pairs not greater than ", L)
    for i in 2:L
        !isprime(i) || continue
        j = divisorsum(i)
        j < i && divisorsum(j) == i || continue
        acnt += 1
        println(@sprintf("%4d", acnt), " => ", j, ", ", i)
    end
end
 
amicables()
 