7406.lean`

Explanation legend Lean4 Domain Explanation Language (L4DEL)

L4DEL explanations are a separate layer. They do not change the Lean source. Intuition is explanatory prose; numbered items are a reading path; sources link the wording back to evidence.

L4DEL: Lean4 Domain Explanation Language

Annotation provenance. This overlay contains 10 curated AI-written annotations and 7190 mechanical source-derived annotations. They have not been human-reviewed as explanations; treat them as unverified and not mathematical authority. Retained generation history: The 71 original curated annotations were produced in a Claude Sonnet 5.5 session at medium effort; Claude Opus 5.5 is recorded in that session as the advisor model, not the direct author. The bulk source-derived expansion was generated mechanically from pinned source comments by tooling developed in a GPT-5.6 Sol session at ultra reasoning; GPT-5.6 Sol did not originate the quoted source prose. On 2026-10-17 the mechanically generated source-comment annotations of the Formal Conjectures, Carleson, FLT, PFR, CompFiles, Mathematics in Lean and Theorem Proving in Lean overlays were regenerated by the same generator after three corrections made in a Claude Sonnet 5.5 session: titles no longer cut a sentence inside mathematics or end on a dangling word, workflow markers are removed from the quoted prose, and declaration names follow the scanner's namespace resolution. The boilerplate step line was dropped, and comments that were only a row of dashes no longer yield annotations. No new prose was written and no human review is claimed.

Credit: The upstream authors and contributors retain credit for the project and mathematics. lean4-explainer only renders their pinned source and adds the separately disclosed explanation layer.

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

7 declarations, 1 contain sorry, 0 declared as axioms

Wolstenholme numbers

Wolstenholme numbers: numerator of $\sum_{k=1}^n \frac{1}{k^2}$.

References:

A007406

Imports (2)

def OeisA7406.a Wolstenholme numbers: numerator of $\sum_{k=1}^n \frac{1}{k^2}$ line 35 source
Source documentation
Wolstenholme numbers: numerator of $\sum_{k=1}^n \frac{1}{k^2}$.

standard axioms: Classical.choice, Quot.sound, propext what this means
Statement uses: Nat
Proof uses: Int.natAbs, Rat.num, Finset.sum, Rat, Finset.Icc, OfNat.ofNat, HDiv.hDiv, HPow.hPow
13 instances, coercions and auxiliary constants left out.
```
def a (n : ℕ) : ℕ :=
…
```
theorem OeisA7406.a_0 line 39 source
extra axioms: _private.0.OeisA7406.a_0._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA7406.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 OeisA7406.a_1 line 42 source
extra axioms: _private.0.OeisA7406.a_1._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA7406.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 OeisA7406.a_2 line 45 source
extra axioms: _private.0.OeisA7406.a_2._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA7406.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 OeisA7406.a_3 line 48 source
extra axioms: _private.0.OeisA7406.a_3._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA7406.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 OeisA7406.a_4 line 51 source
extra axioms: _private.0.OeisA7406.a_4._native.decide.ax_1 what this means
Statement uses: Eq, Nat, OeisA7406.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 OeisA7406.conjecture Conjecture: for $n > 3$, $\gcd(n, a(n-1)) = \text{A089026}(n)$ sorry line 58 source
Source documentation
Conjecture: for $n > 3$, $\gcd(n, a(n-1)) = \text{A089026}(n)$.
- Amiram Eldar and Thomas Ordowski, Jul 28 2019
depends on sorry what this means
Statement uses: Nat, LT.lt, OfNat.ofNat, Eq, Nat.gcd, OeisA7406.a, HSub.hSub, OeisA89026.a
Proof uses: sorryAx, Lean.Name, Bool.false, Lean.Name.num, Lean.Name.str, Lean.Name.anonymous
8 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) (hn : 3 < n) :
    Nat.gcd n (a (n - 1)) = OeisA89026.a n := by
…
```
Mentions: OeisA7406.a, OeisA89026.a