# More problems in 2016 part 5

$\large\sum_{d\mid 29233}\frac{\phi(\phi(d))}{\phi(d)}$

Given that the sum above is equal to $$\dfrac pq$$, where $$p$$ and $$q$$ are coprime positive integers, find $$p+q+2720$$.

Clarification

• The sum is taken over all positive integer divisors $$d$$ of $$29233 = 23 \times31\times41$$.

• $${\phi (\cdot)}$$ denotes the Euler's totient function.

• $$a\mid b$$ denotes "$$a$$ divides $$b$$".

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