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References for this recursive def. of Riemann prime counting function?

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  • kenzi_x
    Hey all. Can anyone point to any references or discussion of this recursive definition (or trivial variants) of the Riemann prime counting function*? In
    Message 1 of 1 , Jul 15, 2013
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      Hey all. Can anyone point to any references or discussion of this recursive definition (or trivial variants) of the Riemann prime counting function*? In Mathematica syntax it's

      P[n_,k_,j_]:=1/k - P[n/j,k+1,Floor[n/j]] + P[n,k,j-1]
      P[n_,k_,1]:=0

      With this, P[n, 1, n] computes the Riemann prime counting function. So N[P[100,1,100]] is 28.5333..., for example. Or DiscretePlot[P[n,1,n],{n,2,100}] is the familiar graph of prime powers up to 100.

      Thanks.

      * http://mathworld.wolfram.com/RiemannPrimeCountingFunction.html
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