import Mathlib

set_option maxHeartbeats 0

open BigOperators Real Nat Topology Rat

theorem amc12a_2021_p25
  (N : ℕ)
  (hN : N > 0)
  (f : ℕ → ℝ)
  (h₀ : ∀ n, 0 < n → f n = ((Nat.divisors n).card)/(n^((1:ℝ)/3)))
  (h₁ : ∀ n ≠ N, 0 < n → f n < f N) :
  (Nat.digits 10 N).sum = 9 := by sorry