Sums of the triple divisor function over values of a ternary quadratic form

Let τ3(n)τ3(n) be the triple divisor function which is the number of solutions of the equation d1d2d3=nd1d2d3=n in natural numbers. It is shown that∑1≤n1,n2,n3≤xτ3(n12+n22+n32)=c1x32(log⁡x)2+c2x32log⁡x+c3x32+Oε(x118+ε) for some constants c1c1, c2c2 and c3c3.