Carmichael function not incrementing k

For any number, the Carmichael function returns 0 no matter what the input n is.

function gcd(a, b)
  if b == 0 then
    return a
  else
    return (gcd(b,a%b))
  end
end

function carmichael(n)
  coprimes = {}
  for i = 1,n-1 do
    if gcd(i,n) == 1 then
      table.insert(coprimes,i)
    end
  end
  k = 0
  while true do
    for counter = 1,#coprimes do
      coprime = coprimes[counter]
      if (coprime^k)%n ~= 1 then
        break
      else
        return k
      end
      k = k+1
    end
  end
end

input = io.read()

print(carmichael(tonumber(input)))

I fixed the code by adding a check to see if the loop was broken and modified the check to make sure that all coprimes met the condition using k, and changed the assignment value of k from 0 to 1, so that coprime^k%n does not always evaluate to 1, because all numbers to the power of 0 result in 1. Modified code:

function carmichael(n)
  coprimes = {}
  for i = 1,n-1 do
    if gcd(i,n) == 1 then
      table.insert(coprimes,i)
    end
  end
  totient = #coprimes
  k = 1
  while k <= totient do
    notcarmichael = false
    for counter = 1,#coprimes do
      coprime = coprimes[counter]
      if (coprime^k)%n ~= 1 then
        notcarmichael = true
        break
      end
    end
    if not notcarmichael then
      return k
    else
      k = k+1
    end
  end
  return totient
end