80326.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

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L4DEL: Lean4 Domain Explanation Language

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Project sources: Pinned project documentation, Formal Conjectures paper, arXiv v1

8 declarations, 1 contain sorry, 0 declared as axioms

Denominator of $\sum_{k=1}^n k^{\mu(k)}$

The sequence $a(n)$ is the denominator of $\sum_{k=1}^n k^{\mu(k)}$, where $\mu$ is the Möbius function.

References:

A080326

Imports (1)

FormalConjecturesUtil

def OeisA80326.term $k^{\mu(k)}$ as a rational number line 37 source
Source documentation
$k^{\mu(k)}$ as a rational number.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat, Rat
Proof uses: Int, ArithmeticFunction, ArithmeticFunction.moebius, ite, Eq, OfNat.ofNat, HDiv.hDiv
12 instances, coercions and auxiliary constants left out.
```
def term (k : ℕ) : ℚ :=
…
```
def OeisA80326.a Denominator of $\sum_{k=1}^n k^{\mu(k)}$ line 44 source
Source documentation
Denominator of $\sum_{k=1}^n k^{\mu(k)}$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Rat.den, Finset.sum, Rat, Finset.Icc, OfNat.ofNat, OeisA80326.term
4 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA80326.a_1 Value of the sequence a at 1 line 49 source
Source documentation
Value of the sequence a at 1.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA80326.a, OfNat.ofNat
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_1 : a 1 = 1 := by
…
```
Mentions: OeisA80326.a
theorem OeisA80326.a_2 Value of the sequence a at 2 line 54 source
Source documentation
Value of the sequence a at 2.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA80326.a, OfNat.ofNat
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_2 : a 2 = 2 := by
…
```
Mentions: OeisA80326.a
theorem OeisA80326.a_3 Value of the sequence a at 3 line 59 source
Source documentation
Value of the sequence a at 3.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA80326.a, OfNat.ofNat
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_3 : a 3 = 6 := by
…
```
Mentions: OeisA80326.a
theorem OeisA80326.a_4 Value of the sequence a at 4 line 64 source
Source documentation
Value of the sequence a at 4.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA80326.a, OfNat.ofNat
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_4 : a 4 = 6 := by
…
```
Mentions: OeisA80326.a
theorem OeisA80326.a_5 Value of the sequence a at 5 line 69 source
Source documentation
Value of the sequence a at 5.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA80326.a, OfNat.ofNat
2 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem a_5 : a 5 = 30 := by
…
```
Mentions: OeisA80326.a
theorem OeisA80326.conjecture Conjecture: $a(n) = \text{primorial}(n)$ for infinitely many $n$ sorry line 75 source
Source documentation
Conjecture: $a(n) = \text{primorial}(n)$ for infinitely many $n$.

depends on sorry what this means
Statement uses: Set.Infinite, Nat, Set.ofPred, Eq, OeisA80326.a, primorial
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous, OfNat.ofNat
1 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
```
theorem conjecture : {n : ℕ | a n = primorial n}.Infinite := by
…
```
Mentions: OeisA80326.a