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Claim. Write $n(n+1)=2^x3^ym$ with $(m,6)=1$. Mohamed Amine Belachhab, Solution to Erdős Problem #933: A Sharp Bound on the 2-3-Smooth Part of n(n+1), Zenodo, 7 February 2026, states as Theorem 1 that $2^x3^y\leq (3/\log 2)\,n\log n$ for every $n\geq 2$, with equality at $n=2$ and $n=8$, and concludes in Corollary 2 that the limsup in Problem 933 equals $3/\log 2\approx 4.328$, so that the answer is no. The argument is a case analysis with the lifting-the-exponent lemma, supported by a computer check up to $10^7$. A second version of 15 February 2026 states the same theorem.

Standing. The claim is rejected. The claimant posted the second version in the site's discussion thread on 15 February 2026, and a reply of the same day by Wouter van Doorn gave the counterexample $n=1487503359=3^{14}\cdot 311$, for which $2^{15}$ exactly divides $n+1$. The {2,3}-part of $n(n+1)$ is then $3^{14}\cdot 2^{15}$, and its ratio to $n\log n$ is about $4.989$, above $3/\log 2$. The Zenodo record was afterwards retitled as a partial solution with a promise to correct the paper, and its text still states Theorem 1.

Depends on. No page of this wiki.