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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. ***********************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 77997, 2231]*) (*NotebookOutlinePosition[ 78681, 2255]*) (* CellTagsIndexPosition[ 78637, 2251]*) (*WindowFrame->Normal*) Notebook[{ Cell[BoxData[ \(\(\( (*\ Here\ are\ some\ of\ the\ calculations\ we\ mentioned\ in\ the\ paper, \ \ in\ particular\ the\ ones\ in\ section\ 3\ \ *) \)\(\[IndentingNewLine]\)\)\)], "Input"], Cell[BoxData[ \(\(\( (*\ The\ Liouville\ \[Lambda] - function\ *) \)\(\[IndentingNewLine]\)\(\[IndentingNewLine]\)\(\ \[Lambda][ p_] := \((faclist = FactorInteger[p]; \((\(-1\))\)^ Sum[faclist[\([i, 2]\)], {i, Length[faclist]}])\)\)\)\)], 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