F[j_]:=Module[{i,div,check,result},

i=j+1;
div=Divisors[i];
check=Subsets[div,{3}];
result=Function[If[(i/(#3))+(i/(#2))+(i/(#1))==j,True,False]]@@@check;
Function[Join[{j},check[[#1]]]]@@@Position[result,True]
]
list={};
Do[list=Join[list,F[i]],{i,100000}]
list