Value of n-th cyclotomic polynomial at n

a(28341) is divisible by 283411^2. What is the next n such that a(n) is not squarefree?

From the catalogue. Imported from The Formal Conjectures Authors (Google DeepMind and contributors) (Apache-2.0) — original. Nobody has started on it here yet: tasks are created as soon as someone asks for one or submits a claim. A Lean proof is checked against the statement below by the Lean kernel; a curator confirms before the problem counts as resolved.

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Cite

@misc{cairn-oeis-70518,
  title        = {Value of n-th cyclotomic polynomial at n},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/oeis-70518}},
  year         = {2026},
  note         = {Open problem on Cairn Commons, CC BY 4.0. Accessed 2026-09-29}
}

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Claims

Verified

Disputed

Refuted

On the literature board

The problem

The question

$a (28341)$ is divisible by $28341 1^{2}$ . What is the next $n$ such that $a (n)$ is not squarefree?

The sequence $a (n) = Φ_{n} (n)$ gives the value of the $n$ -th cyclotomic polynomial evaluated at $n$ : $a (n) = ∣ Φ_{n} (n) ∣$

Formal statement (Lean 4)

From Formal Conjectures, module FormalConjectures.OEIS.«70518». answer(sorry) marks a yes/no question: a proof of the statement on the right of ↔, or of its negation, answers it.

theorem conjecture :
    answer(sorry) =
      if h : ∃ n, 28341 < n ∧ ¬ Squarefree (a n) then
        some (sInf {n | 28341 < n ∧ ¬ Squarefree (a n)})
      else
        none

What counts as progress

A Lean proof of the pinned statement (or of its negation, for a yes/no question) — checked by the Lean kernel against the upstream statement; a curator confirms before the problem is marked resolved.
Partial results: special cases, weaker bounds, reductions — as verified claims.
Computations and numerical evidence with published code (reproducible).
Literature: the problem may have been solved or partly solved already. Report it as a literature claim.
A precise flaw in the formal statement (a misformalisation) — report it upstream too.

References

A070518

Source and licence

Imported from Formal Conjectures (OEIS), commit e6d1743831c2. Statements and descriptions © The Formal Conjectures Authors, Apache License 2.0; reformatted for this page.