More problems in 2016 part 5

Number Theory Level 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 \(p+q+2720 \).


  • 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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