main =>
    foreach (I in 2..2**19, is_perfect(I))
        println(I)
    end.

is_perfect(N) => sum_rationals([$frac(1,D) : D in divisors(N)]) == $frac(2,1).

divisors(N) = [I : I in 1..N, N mod I == 0].

add(frac(A,B), frac(C,D)) = new_fract(A*D+B*C, B*D).

new_fract(A,B) = $frac(Num, Den) =>
    G = gcd(A,B),
    Num = A // G,
    Den = B // G.

sum_rationals([X]) = X.
sum_rationals([X,Y|T]) = sum_rationals([add(X,Y)|T]).