Theorems · Definition · number theory
Nat.smoothNumbers
ℕ → Set ℕ
smoothNumbers n is the set of `n`-smooth positive natural numbers, i.e., the
positive natural numbers all of whose prime factors are less than n.
- Defined in
- Mathlib.NumberTheory.SmoothNumbers
- Cited by
- 32 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.ofPredproof · cited by 6,101
- Nat.primeFactorsListproof · cited by 105
Cited by35
Results whose statement or proof uses this declaration.
- Nat.smoothNumbers_eq_factoredNumbersstatement · cited by 16
- Nat.roughNumbersUpToproof · cited by 5
- Nat.smoothNumbersUpToproof · cited by 5
- Nat.equivProdNatSmoothNumbersstatement · cited by 2
- Nat.ne_zero_of_mem_smoothNumbersstatement and proof · cited by 2
- Nat.smoothNumbersUpTo_card_add_roughNumbersUpTo_cardproof · cited by 1
- Nat.smoothNumbersUpTo_subset_imageproof · cited by 1
- Nat.smoothNumbers_eq_factoredNumbers_primesBelowstatement · cited by 1
- Nat.smoothNumbers_succstatement · cited by 1
- Nat.smoothNumbers_zerostatement · cited by 1
- Nat.Prime.smoothNumbers_coprimestatement and proof · cited by 1
- Nat.primeFactors_subset_of_mem_smoothNumbersstatement and proof · cited by 1