Conjectures associated with A063880

All members of the sequence satisfy n ≡ 108 pmod216.

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.

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Cite

@misc{cairn-oeis-63880,
  title        = {Conjectures associated with A063880},
  author       = {{Cairn Commons contributors}},
  howpublished = {\url{https://cairn-commons.com/problems/oeis-63880}},
  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

mod_216_of_a. All members of the sequence satisfy $n \equiv 108 (mod 216)$ .

unique_primitive_108. $108$ is the only primitive term.

A063880 lists numbers $n$ such that $σ (n) = 2 \cdot usigma (n)$ , where $σ (n)$ is the sum of all divisors and $usigma (n)$ is the sum of unitary divisors.

Equivalently, these are numbers whose unitary and non-unitary divisors have equal sum.

The conjectures state that all members satisfy $n \equiv 108 (mod 216)$ , and that all primitive terms (those whose proper divisors aren't in the sequence) are powerful numbers, with $108$ being the only primitive term.

Formal statement (Lean 4)

From Formal Conjectures, module FormalConjectures.OEIS.«63880» (2 statements).

theorem mod_216_of_a {n : ℕ} (h : A n) : n % 216 = 108

theorem unique_primitive_108 {n : ℕ} (h : IsPrimitiveTerm n) : n = 108

What counts as progress

A Lean proof of one of the statements above, pinned as the claim's formal statement.
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

A063880

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.