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 $$2S_n neq mathbf {N}$$?