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Möbius Inversion Formula
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What is the Möbius function?
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A
A function that takes a positive integer as input and returns 1 if the integer is square-free, -1 if the integer has an even number of prime factors, and 0 otherwise.
💡 Explanation:
The Möbius function is defined as follows: ( \mu(n) = \begin{cases} 1 & \text{if } n \text{ is square-free} \ -1 & \text{if } n \text{ has an even number of prime factors} \ 0 & \text{otherwise} \end{cases} )