erdos_394_part_b

Is it true that, for $k\geq 2$, $\sum_{n\leq x}t_{k+1}(n) =o\left(\sum_{n\leq x}t_k(n)\right)?$

theorem erdos_394_part_b :
    answer(sorry) ↔
      ∀ k ≥ 2, (fun (x : ℝ) ↦ ∑ n ∈ Icc 1 ⌊x⌋₊,
      (t (k + 1) n : ℝ)) =o[atTop]
      (fun (x : ℝ) ↦ ∑ n ∈ Icc 1 ⌊x⌋₊,
      (t k n : ℝ))

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