pith. machine review for the scientific record. sign in
theorem proved term proof

bigOmega_pow

show as:
view Lean formalization →

No prose has been written for this declaration yet. The Lean source and graph data below render without it.

generate prose now

formal statement (Lean)

 276theorem bigOmega_pow {n k : ℕ} : bigOmega (n ^ k) = k * bigOmega n := by

proof body

Term-mode proof.

 277  simp only [bigOmega]
 278  exact ArithmeticFunction.cardFactors_pow
 279
 280/-! ### Liouville function λ -/
 281
 282/-- The Liouville function λ(n) = (-1)^Ω(n).
 283Note: We define this directly since Mathlib may not have a prebuilt version. -/

depends on (1)

Lean names referenced from this declaration's body.