Erdős Problem #845

Let \(C > 0\). Is it true that the set of integers of the form \(n = b_1 + \cdots + b_t\), with \(b_1 < \cdots < b_t\), where \(b_i = 2^{k_i}3^{l_i}\) for \(1 \leq i\leq t\) and \(b_t \leq Cb_1\) has density \(0\)? van Doorn and Everts \cite{vDEv25} have disproved this with \(C=6\) - in fact, they prove that all integers can be written as such a sum in which \(b_t<6b_1\). This was formalized in Lean by Alexeev using Aristotle.