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import FormalConjecturesUtil
namespace OeisA110566open Nat Finset Rat
The primary defining sequence a.
$a(n) = \frac{\operatorname{lcm}_{k=1}^n k}{\operatorname{den}(H_n)}$
def a (n : ℕ) : ℕ :=
(Icc 1 n).lcm id / (harmonic n).denTerm theorems verifying the first few values of the sequence against the official OEIS b-file
@[category test, AMS 11]
theorem a_1 : a 1 = 1 := ⊢ a 1 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_2 : a 2 = 1 := ⊢ a 2 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_3 : a 3 = 1 := ⊢ a 3 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_4 : a 4 = 1 := ⊢ a 4 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_5 : a 5 = 1 := ⊢ a 5 = 1 All goals completed! 🐙@[category test, AMS 11]
theorem a_6 : a 6 = 3 := ⊢ a 6 = 3 All goals completed! 🐙It is conjectured that every odd number occurs in this sequence.
@[category research open, AMS 11]
theorem conjecture :
∀ m : ℕ, Odd m → ∃ n > 0, a n = m := ⊢ ∀ (m : ℕ), Odd m → ∃ n > 0, OeisA110566.a n = m
All goals completed! 🐙end OeisA110566