Number Theory – positive integer sum of two positive integers relatively first to $ n $

Let $ n $ to be a relatively positive integer relatively first to $ 6 $. Let $ S_n $ is the set of positive integers that are relatively prime to $ n $. Consider the sumset $ 2S_n: = {a + b, a, b in S_n } $. For who $ n $ (if such $ n $ even exists) have we $ 2S_n neq mathbf {N} $?