41.lean`

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8 declarations, 1 contain sorry, 0 declared as axioms

No powers as partition numbers

There are no partition numbers $a(k)$ of the form $x^m$, with $x,m$ integers $>1$.

Reference: A41

Imports (2)

Imported by 1 file

FormalConjectures/Subsets/FC100OpenSet1.lean

def OeisA41.a The n-th partition number line 37 source
Source documentation
The n-th partition number.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Fintype.card, Nat.Partition
1 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ := Fintype.card (Nat.Partition n)
…
```
theorem OeisA41.a_0 line 40 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA41.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA41.a_1 line 43 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA41.a, OfNat.ofNat
Proof uses: of_decide_eq_true, id, Bool, Decidable.decide, Bool.true, Eq.refl
3 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA41.a_2 line 46 source
extra axioms: _private.0.OeisA41.a_2._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA41.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA41.a_3 line 49 source
extra axioms: _private.0.OeisA41.a_3._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA41.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA41.a_4 line 52 source
extra axioms: _private.0.OeisA41.a_4._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA41.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA41.a_5 line 55 source
extra axioms: _private.0.OeisA41.a_5._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA41.a, OfNat.ofNat
Proof uses: of_decide_eq_true
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.
theorem OeisA41.noPowerPartitionNumber There are no partition numbers $a(k)$ of the form $x^m$, with $x,m$ integers $>1$ sorry line 62 source
Source documentation
There are no partition numbers $a(k)$ of the form $x^m$, with $x,m$ integers $>1$. See comment by Zhi-Wei Sun (Dec 02 2013).

depends on sorry what this means
Statement uses: Iff, True, Nat, Not, Nat.IsPerfectPower, OeisA41.a
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 noPowerPartitionNumber : answer(sorry) ↔ ∀ k, ¬IsPerfectPower (a k) := by
…
```
Mentions: OeisA41.a