local int = require "int"
require "rat"

local one <const> = rat.of(1)
print("The following numbers (less than 2^19) are perfect:")
for i = 2, (1 << 19) - 1 do
    local sum = rat.of(1, i)
    local divs = int.divisors(i, true)
    divs:remove(1)
    for divs as j do sum += rat.of(1, j) end
    if sum == one then print($"  {i}") end
end