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Claim. Let $A(x)$ count the integers $n\le x$ that are sums of two squarefull numbers. V. Blomer, Binary quadratic forms with large discriminants and sums of two squareful numbers, J. Reine Angew. Math. 569 (2004), 213–234, proves

$$x(\log x)^{-0.253}\ll A(x)\ll x(\log x)^{-1/6}\log\log x,$$

as zbMATH's review of the paper records the bounds. Since $0.253<1/2$, the lower bound alone gives $A(x)\sqrt{\log x}/x\to\infty$, so $A(x)$ is not asymptotic to $c\,x/\sqrt{\log x}$ for any $c>0$. This disproves Problem 1081 independently of [[problems/diophantine_problems/E1081/claims/1981_01_01_odoni|Odoni's earlier disproof]]. The exponent $1-2^{-1/3}+o(1)$ for $A(x)$ is not in this paper; it is proved in Blomer's sequel, J. London Math. Soc. (2) 71 (2005), 69–84.

Depends on. No other wiki page; the claim rests on the cited paper.

Acceptance. Refereed: the paper appeared in the Journal für die reine und angewandte Mathematik (Crelle's journal), volume 569, issued 30 January 2004 according to its Crossref record. Not reviewed: the site's curator credits Odoni with the disproof and lists Blomer's paper among the later estimates for $A(x)$, which is not a credit for the disproof.