File:Aliquot sums and untouchable numbers.pdf

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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}
Date
Source Own work
Author Shreevatsa

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w:en:Creative Commons
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26 August 2023

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8847bc3f18b9d2705a2976d2a42f261e312a20b8

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current23:40, 26 August 2023Thumbnail for version as of 23:40, 26 August 2023360 × 1,385 (7 KB)imagescommonswiki>ShreevatsaUsed scalebox to correct for poor rasterization

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