#Factor, <s>120</s> 113 bytes

I've spent class golfing this and I can't get it shorter.

Translation of: [Julia](http://codegolf.stackexchange.com/a/67876/46231).

    [ [a,b] dup append 2 <combinations> [ members ] keep [ first2 coprime? ] filter [ length ] bi@ 2 /i 1 + swap /f ]

Example runs on the first 5 test cases (a value of 1000 causes it to freeze the editor, and I can't be bothered to compile an executable right now):


    ! with floating point division
    IN: scratchpad auto-use {
          1    
          2    
          4    
          10   
          100  
        }
        [ 
          [1,b] dup append 2 <combinations> [ members ] keep 
          [ first2 coprime? ] filter [ length ] bi@ 2 /i 1 + swap /f 
        ]
        map

    --- Data stack:
    { 1.0 0.75 0.6875 0.63 0.6087 }
    ! with rational division
    IN: scratchpad auto-use {
          1    
          2    
          4    
          10   
          100  
        }
        [ 
          [1,b] dup append 2 <combinations> [ members ] keep 
          [ first2 coprime? ] filter [ length ] bi@ 2 /i 1 + swap / 
        ]
        map
        
    --- Data stack:
    { 1.0 0.75 0.6875 0.63 0.6087 }
    { 1 3/4 11/16 63/100 6087/10000 }