plotting - Plot counting function semi primes

I am trying to generate a plottable semi-prime counting function.

Have tried:

DiscretePlot[Gather[{a = PrimeOmega[Range[100]];
b = PrimeNu[Range[100]];
Count[Transpose[{a, b}], {2, 2}]}
+
{a = PrimeOmega[Range[100]];
b = PrimeNu[Range[100]];
Count[Transpose[{a, b}], {2, 1}]}],{x, 0, 15}, Filling -> Bottom]]

but really have no clue as to where to go from here!

Answer

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

enter image description here

Makes quite a nice comparison

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