Theorems · Theorem · number theory
ArithmeticFunction.IsMultiplicative.prodPrimeFactors_one_add_of_squarefree
∀ {R : Type u_1} [inst : CommSemiring R] {f : ArithmeticFunction R},
f.IsMultiplicative → ∀ {n : ℕ}, Squarefree n → ∏ p ∈ n.primeFactors, (1 + f p) = ∑ d ∈ n.divisors, f d- Cited by
- 1 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- CommSemiringstatement and proof · cited by 10,911
- Finset.sumstatement and proof · cited by 5,195
- Nat.cast_oneproof · cited by 2,501
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidWithZeroproof · cited by 913
- 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
- Nat.Prime.ne_zeroproof · cited by 109
Cited by1
Results whose statement or proof uses this declaration.