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PrimePi




Mathematica Notation

Traditional Notation









Number Theory Functions > PrimePi[x] > Series representations > Other series representations





http://functions.wolfram.com/13.04.06.0010.01









  


  








Input Form





PrimePi[x] == Sum[Floor[EulerPhi[k]/(k - 1)], {k, 2, Floor[x]}]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["PrimePi", "[", "x", "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "2"]], RowBox[List["Floor", "[", "x", "]"]]], RowBox[List["Floor", "[", FractionBox[RowBox[List["EulerPhi", "[", "k", "]"]], RowBox[List["k", "-", "1"]]], "]"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <semantics> <mi> &#960; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Pi]&quot;, PrimePi] </annotation> </semantics> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> k </mi> <mo> = </mo> <mn> 2 </mn> </mrow> <mrow> <mo> &#8970; </mo> <mi> x </mi> <mo> &#8971; </mo> </mrow> </munderover> <mrow> <mo> &#8970; </mo> <mfrac> <mrow> <semantics> <mi> &#981; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Phi]&quot;, EulerPhi] </annotation> </semantics> <mo> ( </mo> <mi> k </mi> <mo> ) </mo> </mrow> <mrow> <mi> k </mi> <mo> - </mo> <mn> 1 </mn> </mrow> </mfrac> <mo> &#8971; </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> PrimePi </ci> <ci> x </ci> </apply> <apply> <sum /> <bvar> <ci> k </ci> </bvar> <lowlimit> <cn type='integer'> 2 </cn> </lowlimit> <uplimit> <apply> <floor /> <ci> x </ci> </apply> </uplimit> <apply> <floor /> <apply> <times /> <apply> <ci> EulerPhi </ci> <ci> k </ci> </apply> <apply> <power /> <apply> <plus /> <ci> k </ci> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PrimePi", "[", "x_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "2"]], RowBox[List["Floor", "[", "x", "]"]]], RowBox[List["Floor", "[", FractionBox[RowBox[List["EulerPhi", "[", "k", "]"]], RowBox[List["k", "-", "1"]]], "]"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2001-10-29