Multiplicative Dilemma Part 1

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

True or False : The above sum converges.

Definitions :

• $\phi(n)$ 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