Note on sums of seven cubes of smooth numbers (Q2910118)

The aim of the paper is to prove that every sufficiently large number \(n\) is a sum of seven cubes such that the cube of the largest prime factor of the product of these, is bounded from above by \(n^s\) where \(s \cdot exp(1)^{1/2}\) is bounded below by an explicit numerical constant \(s_0.\) One has \(s_0 = 0.835239 \ldots,\) improving on an analogue result of the author. Indeed \(s_0\) lies in \(\mathbb{Q}[d]\) where \(d=\sqrt{2833},\) and exactly we have NEWLINE\[NEWLINE 85977 \cdot s_0 = (-2784931 + 53672 \cdot d). NEWLINE\]