local int = require "int"

local function is_perfect(n)
    if n <= 2 then return false end
    local tot = 1
    for i = 2, math.floor(math.sqrt(n)) do
        if n % i == 0 do
            tot += i
            local q = n // i
            if q > i then tot += q end
        end
    end
    return n == tot
end

print("The first seven perfect numbers are:")
local count = 0
local p = 2
while count < 7 do
    local n = (1 << p) - 1
    if int.isprime(n) then
        n *= 1 << (p - 1)
        if is_perfect(n) then
            io.write($"{n} ")
            count += 1
        end
    end
    p += 1
end
print()