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Summary
DescriptionAliquot sums and untouchable numbers.pdf
English: Diagram showing the map from positive integers to their aliquot sums (sum of all proper divisors), highlighting the "untouchable numbers" 2 and 5 that are not in the image. Source code:
\documentclass{standalone}\usepackage{graphicx}% for \scalebox\usepackage{tikz}\usetikzlibrary{arrows.meta}% for more arrow tip styles\begin{document}\scalebox{2.0}{% scale factor for Mediawiki rasterization\begin{tikzpicture}[>={Stealth}, every node/.style={circle, draw, minimum size=0.5cm}, yscale=-1]
% Nodes on the left\node (L1) at (0,1) {1};
\node (L2) at (0,2) {2};
\node (L3) at (0,3) {3};
\node (L4) at (0,4) {4};
\node (L5) at (0,5) {5};
\node (L6) at (0,6) {6};
\node (L7) at (0,7) {7};
\node (L8) at (0,8) {8};
\node (L9) at (0,9) {9};
\node (L10) at (0,10) {10};
% Ellipsis\node[draw=none] at (0,11) {\vdots};
% Nodes on the right\node[fill=green!40] (R0) at (2,0) {0};
\node[fill=green!40] (R1) at (2,1) {1};
\node[fill= red!40] (R2) at (2,2) {2};
\node[fill=green!40] (R3) at (2,3) {3};
\node[fill=green!40] (R4) at (2,4) {4};
\node[fill= red!40] (R5) at (2,5) {5};
\node[fill=green!40] (R6) at (2,6) {6};
\node[fill=green!40] (R7) at (2,7) {7};
\node[fill=green!40] (R8) at (2,8) {8};
% Ellipsis\node[draw=none] at (2,9) {\vdots};
% Edges\begin{scope}\draw[>->] (L1) -- (R0);
\draw[>->] (L2) -- (R1);
\draw[>->] (L3) -- (R1);
\draw[>->] (L4) -- (R3);
\draw[>->] (L5) -- (R1);
\draw[>->] (L6) -- (R6);
\draw[>->] (L7) -- (R1);
\draw[>->] (L8) -- (R7);
\draw[>->] (L9) -- (R4);
\draw[>->] (L10) -- (R8);
\end{scope}\end{tikzpicture}}% end of \scalebox\end{document}
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