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Erdős problem 457

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Is there some ϵ>0\epsilon > 0 such that there are infinitely many nn where all primes p≤(2+ϵ)log⁡np \le (2 + \epsilon) \log n divide ∏1≤i≤log⁡n(n+i)? \prod_{1 \le i \le \log n} (n + i)?

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Problem row
sha256:45fe4023fa39e59701f79185b08321dbc0c51adcdbe26874b866c99710a0a961
Metadata
sha256:bcc3428da9552f154ae8028e7b884a1a6d3c5bbc5335d2361a6b38543627292f
Observation
sha256:9c8326e865b6017b103af7611c852a06776d81964979b8ab5a1b800cd550dff6
Content
sha256:59eed676b7ab506bd3a09f2c3f032df8ca9d81dde53bfdbced7a3ae4c01f047a
Repository
sha256:a956b84c437202e5a02cc9e036a621bd14a302b34a75758115730bdbb77c52a4
Projection
sha256:a4a96441668a9f8b33afbcb3f696a2639f5fae145f36ddc063d7f67d5fb87ce8
Source commit
36c6d0fef71a3fec84d9dcd5eeca4e22e378f7cb
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