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Running least common multiples: distinct values and multiplicities
Cook, Will, Running least common multiples: distinct values and multiplicities, July 2026, revised 5 October 2026, 73-page author-hosted edition.
The opening distinguishes the reciprocal sum over distinct running LCMs from the sum retaining every smooth-number multiplicity. It reports irrationality for the distinct-value sum at {2,3,5}, and a two-prime Hecke–Mahler reduction credited to prior work. Its residue criterion for the repeated three-prime sum leaves the required arithmetic condition open. These assertions are source-reported, with no verification tier assigned here.
The PDF was obtained from the author's public download address above. No explicit license was located on that download page or by searching the PDF text for license or copyright terms; the holding term is unstated. No file of this source is held.
Read status. The public PDF abstract and opening statements on pages 1–2 were read. The kernel arguments and full proofs have not been checked here.
Source: https://wcook04.github.io/plectis/papers/erdos269-running-lcm-reasoning-surface.pdf.
Bears on. Problem 269: the stated scope above supplies a related result or a limitation of a possible route.