efficient_divisors.rb

def list_squared(m, n)
  divs_hash = {}
  (m..n).reduce([]) do |result, i|
    sum = 1
    divs = [1]
    for k in (2..i/2)
      if (i % k).zero?
        current = (i/k)
        if divs_hash.has_key?(current.to_s)
          divs_hash[current.to_s].each do |c|
            unless divs.include?(c)
              divs.push(c)
              sum += c*c
            end
          end
        end
        unless divs.include?(k)
          divs.push(k)
          sum += k*k
        end
      end
    end
    unless i == 1
      divs.push(i)
      sum += i*i
    end

    divs_hash[i.to_s] = divs
    number = Math.sqrt(sum)
    number == number.to_i ? result.push([i, sum]) : result
  end
end