erdos_295

Let $k(N)$ denote the smallest $k$ such that there exists $N ≤ n_1 < ⋯ < n_k$ with $\frac 1 {n_1} + ... + \frac 1 {n_k} = 1$ Is it true that $\lim_{N \to \infty} k(N) - (e - 1)N = \infty$?

theorem erdos_295 :
    answer(sorry) ↔ Filter.atTop.Tendsto (fun N => k N - (rexp 1 - 1)*N) Filter.atTop

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