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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.06764 |
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Table of Contents:
- For $k\geq 2$, we give a detailed exposition of the superior $k$-highly composite numbers. We then consider the function \[f_k(n)=\frac{\log d_k(n)\log\log n}{\log k\log n},\quad n\geq 3\] which has a maximum value $λ(k)$ at a superior $k$-highly composite number. We develop an efficient algorithm to compute $λ(k)$ and the positive integer $N_{\max}(k)$ where $f_k$ achieves the value $λ(k)$. The results for $2\leq k\leq 100$ are tabled.