Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a ≠ b, then a and b are an amicable pair and each of a and b are called amicable numbers.

For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.

Evaluate the sum of all the amicable numbers under 10000.



In [23]:

    
let isDivisor x y = x % y = 0

let d n = 
    [1 .. (n-1)] 
    |> List.filter (isDivisor n)
    |> List.sum    

let isAmicable n = 
    let d_n = d n
    let d_d_n = (d(d_n))
    (n = d_d_n) && (n <> d_n)

[1..10000]
|> List.filter isAmicable
|> List.sum









    Out[23]:





31626



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