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Divisibility Set of the Generalized Euler Totient

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?

Exact FrontierDelta

Prior state unknownproved

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Occurred: Jun 1, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: Divisibility Set of the Generalized Euler Totient · Totient divisibility

Confidence: Not scored

Registry verification: unreviewed · preprint · resolved

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VibeMathed
registry · event recorded by

John M. Campbell
human · human collaborator

GPT-5.5 Pro
model · ai model contributor · OpenAI

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This event attributed to John M. Campbell

This event attributed to GPT-5.5 Pro

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Divisibility Set of the Generalized Euler Totient — Mathematical Frontier Network