In this article, we introduce an algorithm proposed by Jakub Pawlewicz [1] to count square free numbers not exceeding $n$ efficiently.

We first introduce a well-known algorithm with time complexity $\tilde{\mathcal{O}}(\sqrt{n})$. After that, we present a algorithm which is a modified version of first algorithm with time complexity $\tilde{\mathcal{O}}(n^{2/5})$ following from [1].

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