Freaks City

Mobius Function Definition \[\mu(n) = \begin{cases} 1 & n = 1 \\ 0 & n \text{ has squared prime factors} \\ (-1)^k & \text{where } k \text{ is the count of distinct prime factors of } n \end{cases}\] Properties The Mobius function is multilpicative: \[\sum_{d \mid n} \mu(d) = \varepsilon(n) \\ \mu \ast 1 = \varepsilon\] where \(\var ...