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Divisibility Set of the Generalized Euler Totient

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generalized-totient-divisibilityNumber theoryposed by Engin Büyükaşik et al., 2024recorded: solved

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Statement

Define φk(n)=∑1≤a≤n,(a,n)=1ak\varphi_k(n) = \sum_{1 \le a \le n, (a,n)=1} a^k and Ds={k≥s:φs(n)∣φk(n) for every n}\mathcal{D}_s = \{k \ge s : \varphi_s(n) \mid \varphi_k(n) \text{ for every } n\}. Is D1={1,3,15}\mathcal{D}_1 = \{1, 3, 15\}, as conjectured by Büyükaşik and collaborators?

Context

A recent question on a generalized totient with a one-paper audience.

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  • #1

    Attempt 1

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