Claims

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2026_04_25_treasure42: A GPT-5.5 Pro argument posted by Treasure42 gives, for almost all n, the bounds log* n << h(n) <= H(n) << log* n, so the ratio H(n)/h(n) stays bounded and the problem's estimate is settled up to constants.

2026_04_26_turturean: David Turturean claims, with a GPT-5.5 Pro argument and a Lean 4 formalization, that h(n) = (1/2 + o(1)) log* n and H(n) = (1 + o(1)) log* n for almost all n, so H(n)/h(n) tends to 2.

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