Odd man out

What is the sum of the first two positive odd integers $$n$$ such that the $$n^\text{th}$$ arithmetic derivative of $$n$$ is non-zero?

For example, the third arithmetic derivative of $$n$$, is given by $$((n')')'$$.

Clarification: The arithmetic derivative of $$n$$ is given by:

• $$n' = 0$$ for $$n$$ = 1 or 0.
• $$n'$$ = 1 if $$n$$ is prime.
• $$n' = a'b + b'a$$ where $$a>1$$ and $$b>1$$ are factors of $$n$$.

Note: If $$n$$ has multiple factors you can choose any pair to get the arithmetic derivative.

(Image courtesy of "Top Lead Generators")

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