Solved on the site: the curator credits Ahlswede and Khachatrian (1996) with proving Erdős's refined conjecture that the maximum is attained, for some $j$, by the integers up to $N$ divisible by one of $2q_1,\ldots,2q_j,q_1\cdots q_j$, where $q_1<\cdots<q_r$ are the prime factors of $N$, after the original guess of Erdős and Graham fell to easy counterexamples; see the claim page (Ahlswede and Khachatrian, 1996). The site notes that the 1973 source printed the condition as $(a,b)=1$, a misprint for $(a,b)>1$. The standing in the frontmatter derives from the claim pages.