Asymptotic count of primitive sums of three squarefull numbers

Establish the conjectured asymptotic formula N(B)\sim cB^{1/2} as B\to\infty for the number N(B) of primitive positive solutions (a,b,c) to a+b=c in which a, b, and c are respectively 2-full, 2-full, and 2-full, for a suitable constant c>0.

Background

The paper defines N(B) as the number of primitive triples (a,b,c) with 1\leq a,b,c\leq B, a+b=c, and each of a, b, and c belonging to the corresponding set of full numbers. When p=q=r=2, these are sums of three powerful (squarefull) numbers, and the associated Campana orbifold is in the log-Fano range.

The authors state that the expected order of growth is cB^{1/2}, but the results in the paper provide only an upper bound with exponent strictly larger than 1/2, namely a bound of the form N(B)\ll_\delta B^{3/5-\delta}. Thus the conjectured asymptotic, including both the precise exponent and the leading constant, remains unresolved.