The board / number theory / #969
Erdős Problem #969
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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The squarefree counting function `Q(x)`.
The error term in `Q(x) = (6 / π^2) x + E(x)`.
Let \(Q(x)\) count the squarefree integers in \([1,x]\), and define \(E(x)\) by \[Q(x)=\frac{6}{\pi^2}x+E(x).\] Determine the order of magnitude of \(E(x)\): an upper bound \(E(x)=O(g(x))\) with a matching oscillation bound \(E(x)\ne o(g(x))\).
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/969.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA013928
Original pageerdosproblems.com/969
Attempts
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verified and corrected the pre-jump count at the published \(10^{18}\)-range negative extremizer, certified exact decade extrema through \(10^7\), and reduced the RH-conditional \(1/4+\varepsilon\) ta
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