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Problem 969 — Erdős Problems

Problem 969

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).

Source: erdosproblems.com/969

Number theory

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Open. The site's label is OPEN (the page was last edited on 2025-10-19, and its proof-claims tab was empty on 2026-10-06), and no claim page is recorded.

EvLi31: Evelyn, C. J. A. and Linfoot, E. H., On a problem in the additive theory of numbers. Ann. of Math. (2) (1931), 261-270.
Li16: Liu, H.-Q., On the distribution of squarefree numbers. J. Number Theory (2016), 202-222.
Wa63: Walfisz, Arnold, Weylsche Exponentialsummen in der neueren Zahlentheorie. (1963), 231.

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Status: Open
Topics: Number theory
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