# 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.

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

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