Divisibility Set of the Generalized Euler Totient

Precise statement

Define $\varphi_k(n) = \sum_{1 \le a \le n, (a,n)=1} a^k$ and $\mathcal{D}_s = \{k \ge s : \varphi_s(n) \mid \varphi_k(n) \text{ for every } n\}$. Is $\mathcal{D}_1 = \{1, 3, 15\}$, as conjectured by Büyükaşik and collaborators?

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.5 Pro

The exact classification was proved via an argument based on interactions with GPT-5.5 Pro.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Author-checked arXiv preprint. Not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-06-01

   arXiv:2606.01633 - On a problem on a generalization of Euler's totient function

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.