smallestCoPrimeOf :: Int -> Int
smallestCoPrimeOf a
  = iterateCandidates a startingCandidate
  where
    startingCandidate = 2
    iterateCandidates :: Int -> Int -> Int
    iterateCandidates a candidate
      | gcd a candidate == 1 = candidate
      | otherwise            = iterateCandidates a (candidate + 1)