256012.lean`

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

7 declarations, 1 contain sorry, 0 declared as axioms

Partitions of $n$ into distinct non-squarefree parts for $n > 23$

a: Number of partitions of $n$ into distinct parts that are not squarefree. This is the number of finite subsets of positive integers $P$ such that $\sum_{k \in P} k = n$ and every element $k \in P$ is not squarefree.

References:

A256012
arxiv/2605.22763 Advancing Mathematics Research with AI-Driven Formal Proof Search by George Tsoukalas et al.

Imports (1)

FormalConjecturesUtil

def OeisA256012.a a: Number of partitions of $n$ into distinct parts that are not squarefree line 45 source
Source documentation
a: Number of partitions of $n$ into distinct parts that are not squarefree. This is the number of finite subsets of positive integers $P$ such that $\sum_{k \in P} k = n$ and every element $k \in P$ is not squarefree.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Finset, SDiff.sdiff, Finset.range, HAdd.hAdd, OfNat.ofNat, Singleton.singleton, Finset.card, Finset.filter, And, Eq, Finset.sum, id, Membership.mem, Not, Squarefree, Finset.powerset
14 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
lemma OeisA256012.a_0 line 58 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA256012.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.
lemma OeisA256012.a_1 line 61 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA256012.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.
lemma OeisA256012.a_2 line 64 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA256012.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.
lemma OeisA256012.a_3 line 67 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA256012.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.
lemma OeisA256012.a_4 line 70 source
standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Eq, Nat, OeisA256012.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 OeisA256012.a_pos_of_gt sorry line 81 source
depends on sorry what this means
Statement uses: Nat, GT.gt, OfNat.ofNat, OeisA256012.a
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
4 instances, coercions and auxiliary constants left out.

Tactic trace: 1 steps
Open to load the checked before-and-after goal states.