Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_sub_of_squarefree
∀ {R : Type u_1} [inst : CommRing R] (f : ArithmeticFunction R),
f.IsMultiplicative →
∀ {n : ℕ}, Squarefree n → ∏ p ∈ n.primeFactors, (1 - f p) = ∑ d ∈ n.divisors, ↑(ArithmeticFunction.moebius d) * f d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommRing
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Finset.sumstatement and proof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- Finset.prodstatement · cited by 2,356
- Finset.prod_congrproof · cited by 646
- ArithmeticFunctionstatement and proof · cited by 290
- Nat.divisorsstatement and proof · cited by 137
- Nat.primeFactorsstatement and proof · cited by 129
- Squarefreestatement and proof · cited by 112
- ArithmeticFunction.IsMultiplicativestatement and proof · cited by 45
- ArithmeticFunction.moebiusstatement and proof · cited by 45
Cited by1
Results whose statement or proof uses this declaration.
- BoundingSieve.inv_selbergTerms_eq_sum_divisors_moebius_nuproof · cited by 1