Multiplicative Dilemma Part 1

Calculus Level 4

\[\Large{ \sum_{n=1}^\infty \frac{\phi(n)}{\tau(n)^{\mu(n)}} }\]

True or False: The above sum converges.


  • \(\phi(n)\) is the number of positive integers not greater than \(n\) that are relatively prime to \(n\) (Euler's totient function).
  • \(\tau(n)\) is the number of positive divisors of \(n\).
  • \(\mu(n)\) is 0 if \(n\) is not squarefree (divisible by a positive square number greater than 1), and otherwise is equal to \((-1)^{\Omega(n)}\) where \(\Omega(n)\) is the number of prime divisors of \(n\).

Try Part 2


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