#Update#

OK - First part of update solved:

    a = PrimeOmega[Range[1000]];
    b = PrimeNu[Range[1000]];
    c = Range[1000];
    ListLinePlot[{c/Zeta[2] - Accumulate[Flatten[Inner[If[#1 === #2, 1, 0] 
    &, a, b, List]]]}, Filling -> Axis]

![enter image description here][1]


... Just unsure how to modify Artes' count plot.


#Old#

Sorry Artes, yes - was looking for this kind of thing: 

    a = PrimeOmega[Range[100]];
    b = PrimeNu[Range[100]];
    ListPlot[{Accumulate[Flatten[Inner[If[#1 === #2, 1, 0] &, a, b, List]]],    
    Accumulate[Flatten[Inner[If[#1 === #2 + 1, 1, 0] &, a, b, List]]],
    Accumulate[Flatten[Inner[If[#1 === #2 + 2, 1, 0] &, a, b, List]]]}]


![enter image description here][2]


  [1]: https://i.sstatic.net/PTfOw.gif
  [2]: https://i.sstatic.net/Lyrjs.gif