The twenty-first Project Euler problem is:

Evaluate the sum of all amicable pairs under 10000.

An amicable pair is two numbers such that the sum of the proper divisors of the first number adds up to the second and vice versa. Each member of the pair is considered to be an amicable number. As always Wikipedia has a good article on the subject.

Following the suggestion from the statement of the problem I define a function d(n) that computes the sum of n's divisors:

let d n =

    {1..n/2} |> Seq.filter (fun i -> n%i = 0) |> Seq.sum

Now I need to test whether a given number is amicable:

let amicable n =

    let sum = d n

    (sum <> n) && (d sum = n)

Note that we exclude so called perfect numbers where the sum of n's divisors is n.

Finally, I can compute the sum of all the amicable numbers under 10,000 as follows:

{1..10000} |> Seq.filter (fun i -> amicable i) |> Seq.sum |> printfn "total = %A"