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DigitCount




Mathematica Notation

Traditional Notation









Number Theory Functions > DigitCount[n,b] > Other identities > Congruence properties





http://functions.wolfram.com/13.10.32.0002.01









  


  








Input Form





Nest[s, n, n] == 15 /; s[n] == DivisorSum[Sum[j DigitCount[d, 10, j], {j, 1, 9}], {d, n}] && Element[n, Integers] && n > 1








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["Nest", "[", RowBox[List["s", ",", " ", "n", ",", " ", "n"]], "]"]], "\[Equal]", "15"]], "/;", RowBox[List[RowBox[List[RowBox[List["s", "[", "n", "]"]], "\[Equal]", RowBox[List["DivisorSum", "[", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "9"], RowBox[List["j", " ", RowBox[List["DigitCount", "[", RowBox[List["d", ",", "10", ",", "j"]], "]"]]]]]], ",", RowBox[List["{", RowBox[List["d", ",", "n"]], "}"]]]], "]"]]]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", ">", "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> <mstyle maxsize='1'> <mrow> <mrow> <mrow> <mrow> <munder> <mrow> <mi> s </mi> <mo> ( </mo> <mrow> <mi> s </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mo> &#8230; </mo> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> s </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <munder> <mo> &#65080; </mo> <mi> n&#8208;times </mi> </munder> </munder> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mstyle> <mo> &#10869; </mo> <mn> 15 </mn> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> s(n) </mi> <mo> &#10869; </mo> <mrow> <munder> <mo> &#8721; </mo> <mrow> <mi> d </mi> <mo> | </mo> <mi> n </mi> </mrow> </munder> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mn> 9 </mn> </munderover> <mrow> <mi> j </mi> <mo> &#8290; </mo> <mrow> <msubsup> <mi> s </mi> <mn> 10 </mn> <mrow> <mo> ( </mo> <mi> j </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> d </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <mrow> <mrow> <mstyle maxsize='1'> <mrow> <mrow> <mrow> <mrow> <munder> <mrow> <mi> s </mi> <mo> ( </mo> <mrow> <mi> s </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mo> &#8230; </mo> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> s </mi> </mrow> </mrow> </mrow> </mrow> </mrow> <munder> <mo> &#65080; </mo> <mi> n&#8208;times </mi> </munder> </munder> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mi> n </mi> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> <mo> ) </mo> </mrow> </mstyle> <mo> &#10869; </mo> <mn> 15 </mn> </mrow> <mo> /; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> s(n) </mi> <mo> &#10869; </mo> <mrow> <munder> <mo> &#8721; </mo> <mrow> <mi> d </mi> <mo> | </mo> <mi> n </mi> </mrow> </munder> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> j </mi> <mo> = </mo> <mn> 1 </mn> </mrow> <mn> 9 </mn> </munderover> <mrow> <mi> j </mi> <mo> &#8290; </mo> <mrow> <msubsup> <mi> s </mi> <mn> 10 </mn> <mrow> <mo> ( </mo> <mi> j </mi> <mo> ) </mo> </mrow> </msubsup> <mo> ( </mo> <mi> d </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> </mrow> <mo> /; </mo> <mrow> <mrow> <mi> n </mi> <mo> &#8712; </mo> <mi> &#8484; </mi> </mrow> <mo> &#8743; </mo> <mrow> <mi> n </mi> <mo> &gt; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["Nest", "[", RowBox[List["s_", ",", "n_", ",", "n_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["15", "/;", RowBox[List[RowBox[List[RowBox[List["s", "[", "n", "]"]], "\[Equal]", RowBox[List["DivisorSum", "[", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "1"]], "9"], RowBox[List["j", " ", RowBox[List["DigitCount", "[", RowBox[List["d", ",", "10", ",", "j"]], "]"]]]]]], ",", RowBox[List["{", RowBox[List["d", ",", "n"]], "}"]]]], "]"]]]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", ">", "1"]]]]]]]]]]


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





2001-10-29