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OP-11917Status unassessedNumber theory

The asymmetric multiplication table with seven or more factors

The asymmetric multiplication table with seven or more factors. Current research status is unassessed. The dated source poses this question; inclusion does not certify that it remains open today.

MSC 11 · Number theory

Editorial MSC2020 mapping of The asymmetric multiplication table with seven or more factors. https://ems.press/content/serial-article-files/52435#page=58 Not an author-supplied code.

Source question · editorial summaryAs of 2025; current status unassessedSource & evidence ↓
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Problem statement

For k≥7k\ge7 and positive integers N1≤⋯≤NkN_1\le\cdots\le N_k, determine the order of magnitude of Ak(N1,…,Nk)=∣{n1⋯nk:1≤ni≤Ni}∣A_k(N_1,\ldots,N_k)=|\{n_1\cdots n_k:1\le n_i\le N_i\}| uniformly in the side lengths. Equal side lengths and the asymmetric cases 2≤k≤62\le k\le6 are distinguished as known in the report.

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References
  1. [1]Problem-session contributors; compiled by Thomas F. Bloom. Oberwolfach 2025 — Analytic Number Theory Problem Session (2025).; The asymmetric multiplication table with seven or more factors linkCC BY-SA 4.0; source contributors, compiled by Thomas F. Bloom. These attributed adaptations are available under the same license.

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