number-theory / Multiplicative number theory
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?
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Append-only history
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?
Research memory
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?
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