euler021.lua

local function divisors_sum(n)
    local sum = 0
    if n > 1 then
        sum = 1
    end
    local k = 2
    while k*k <= n do
        if n % k == 0 then
            sum = sum + k + n/k
            if k*k == n then
                sum = sum - k
            end
        end
        k = k + 1
    end
    return sum
end

function is_amicable(n)
    local d = divisors_sum(n)
    return d ~= n and divisors_sum(d) == n
end

local max_n = 1000000
local sum = 0
for n = 2, max_n do
    if is_amicable(n) then
        sum = sum + n
    end
end

print(sum)