A closer look at some new identities - Geoffrey B. Campbell (International Journal of Mathematics and Mathematical Sciences)
We obtain infinite products related to the concept of visible from the origin point vectors. Among these is ∏k=3∞(1−Z)φ,(k)/k=11−Zexp(Z32(1−Z)2−12Z−12Z(1−Z)),  |Z|<1, in which φ3(k) denotes for fixed k, the number of positive integer solutions of (a,b,k)=1 where a<b<k, assuming (a,b,k) is the gcd(a,b,k).