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 = 1 1 − Z exp ( Z 3 2 ( 1 − Z ) 2 − 1 2 Z − 1 2 Z ( 1 − Z ) ) ,     | Z | < 1 , in which φ 3 ( 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 ) .