Theorems · Theorem · number theory
ArithmeticFunction.sigma_eq_prod_primeFactors_sum_range_factorization_pow_mul
∀ {k n : ℕ},
n ≠ 0 → (ArithmeticFunction.sigma k) n = ∏ p ∈ n.primeFactors, ∑ i ∈ Finset.range (n.factorization p + 1), p ^ (i * k)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites15
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
- Finsuppstatement · cited by 5,255
- Finset.sumstatement and proof · cited by 5,195
- Finset.prodstatement and proof · cited by 2,356
- Finset.rangestatement and proof · cited by 1,341
- Finset.prod_congrproof · cited by 646
- ArithmeticFunctionstatement · cited by 290
- Nat.factorizationstatement and proof · cited by 215
- Nat.primeFactorsstatement and proof · cited by 129
- ArithmeticFunction.sigmastatement and proof · cited by 40
- Nat.prime_of_mem_primeFactorsproof · cited by 29
- ArithmeticFunction.IsMultiplicative.multiplicative_factorizationproof · cited by 6
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