Theorems · Theorem · number theory
Nat.sum_divisorsAntidiagonal
∀ {M : Type u_1} [inst : AddCommMonoid M] (f : ℕ → ℕ → M) {n : ℕ},
∑ i ∈ n.divisorsAntidiagonal, f i.1 i.2 = ∑ i ∈ n.divisors, f i (n / i)- Defined in
- Mathlib.NumberTheory.Divisors
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Nat.divisorsstatement and proof · cited by 137
- Finset.sum_mapproof · cited by 115
- Nat.divisorsAntidiagonalstatement · cited by 61
- Nat.map_div_right_divisorsproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- Nat.sum_divisorsAntidiagonal'proof · cited by 3
- ArithmeticFunction.coe_zeta_mul_commproof · cited by 2
- tsum_prod_pow_eq_tsum_sigmaproof · cited by 2
- BoundingSieve.inv_selbergTerms_eq_sum_divisors_moebius_nuproof · cited by 1
- ArithmeticFunction.IsMultiplicative.prodPrimeFactors_add_of_squarefreeproof · cited by 1
- ArithmeticFunction.sum_moebius_mul_log_eqproof · cited by 0