For distinct integers m < n, if rad(m+i) = rad(n+i) for all i ≤ k, then k ≪ (log n)^{3/2}/(log log n)^{9/2}, improving a 1989 bound.
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On pairs of consecutive sequences with the same radicals
For distinct integers m < n, if rad(m+i) = rad(n+i) for all i ≤ k, then k ≪ (log n)^{3/2}/(log log n)^{9/2}, improving a 1989 bound.