theorem
proved
term proof
vonMangoldt_sum_divisors
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formal statement (Lean)
761theorem vonMangoldt_sum_divisors {n : ℕ} :
762 ∑ d ∈ n.divisors, vonMangoldt d = Real.log n := by
proof body
Term-mode proof.
763 simp only [vonMangoldt]
764 exact ArithmeticFunction.vonMangoldt_sum
765
766/-! ### Sigma multiplicativity helpers -/
767
768/-- σ_k(mn) = σ_k(m) × σ_k(n) for coprime m, n. -/