Erdős Problem #969

declared status 'open'. Formalized: no. Let $Q(x)$ count the number of squarefree integers in $[1,x]$. Determine the order of magnitude in the error term in the asymptotic$$Q(x)=\frac{6}{\pi^2}x+E(x).$$ Current best: The best known unconditional upper bound is of the shape $x^{1/2-o(1)}$, due to Walfisz [Wa63]. Conditional on this assumption, the best known upper bound is$$E(x)\ll x^{\frac{11}{35}+o(1)},$$due to Liu [Li16]. Prize: no. OEIS: A013928. Tags: number theory.

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