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import FormalConjecturesUtil$\gcd(\mathrm{numerator}(H_n), n!)$
$a(n) = \gcd(\mathrm{A001008}(n), n!)$, where $\mathrm{A001008}(n)$ is the numerator of the $n$-th harmonic number $H_n = \sum_{i=1}^n \frac{1}{i}$.
References:
namespace OeisA93818$a(n) = \gcd(\mathrm{numerator}(H_n), n!)$, where $H_n$ is the $n$-th harmonic number.
def a (n : ℕ) : ℕ :=
Nat.gcd (harmonic n).num.natAbs n.factorial
Value of the sequence a at 0.
@[category test, AMS 11]
theorem a_0 : a 0 = 1 := ⊢ a 0 = 1 All goals completed! 🐙
Value of the sequence a at 1.
@[category test, AMS 11]
theorem a_1 : a 1 = 1 := ⊢ a 1 = 1 All goals completed! 🐙
Value of the sequence a at 2.
@[category test, AMS 11]
theorem a_2 : a 2 = 1 := ⊢ a 2 = 1 All goals completed! 🐙
Value of the sequence a at 3.
@[category test, AMS 11]
theorem a_3 : a 3 = 1 := ⊢ a 3 = 1 All goals completed! 🐙
Value of the sequence a at 4.
@[category test, AMS 11]
theorem a_4 : a 4 = 1 := ⊢ a 4 = 1 All goals completed! 🐙Conjecture: Every odd prime occurs as a term in the sequence.
@[category research open, AMS 11]
theorem conjecture (p : ℕ) (hp : p.Prime) (hp_odd : p ≠ 2) : ∃ n > 0, a n = p := p:ℕhp:Nat.Prime php_odd:p ≠ 2⊢ ∃ n > 0, a n = p
All goals completed! 🐙end OeisA93818