Claims

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1989_03_01_erdos_tenenbaum: For almost all n the count of coprime consecutive divisor pairs exceeds a power of log n, so its ratio to omega(n) tends to infinity, and its maximum up to x is at least exp of order log x over (log log x) squared.

2026_07_31_korsky: The maximum of the coprime-consecutive-divisor count up to x is exp(Theta(log x / log log x)), with an explicit lower constant, answering Erdős's maximal-order questions in the negative; prepared with GPT-5.6 Pro.

2026_08_04_ross: For squarefree n with k prime factors the maximum number of coprime consecutive divisor pairs is at least c phi^k/root k; the base phi already follows, with F_{k+1}, from Chevyrev, Searles and Slinko (2013).

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