MoebiusMu[n] == 0 /; Exists[m, Element[n/m^2, Integers]]

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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <semantics> <mi> &#956; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[Mu]&quot;, MoebiusMu] </annotation> </semantics> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> <mo> &#10869; </mo> <mn> 0 </mn> </mrow> <mo> /; </mo> <mrow> <msub> <mo> &#8707; </mo> <mi> m </mi> </msub> <mrow> <mfrac> <mi> n </mi> <msup> <mi> m </mi> <mn> 2 </mn> </msup> </mfrac> <mo> &#8712; </mo> <semantics> <mi> &#8484; </mi> <annotation encoding='Mathematica'> TagBox[&quot;\[DoubleStruckCapitalZ]&quot;, Function[Integers]] </annotation> </semantics> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <ci> MoebiusMu </ci> <ci> n </ci> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <exists /> <bvar> <ci> m </ci> </bvar> <apply> <in /> <apply> <times /> <ci> n </ci> <apply> <power /> <apply> <power /> <ci> m </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MoebiusMu", "[", "n_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List["0", "/;", RowBox[List[SubscriptBox["\[Exists]", "m"], RowBox[List[FractionBox["n", SuperscriptBox["m", "2"]], "\[Element]", "Integers"]]]]]]]]]]

2001-10-29