File:Aliquot sums and untouchable numbers.pdf
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Aliquot_sums_and_untouchable_numbers.pdf (file size: 7 KB, MIME type: application/pdf)
This file is from Wikimedia Commons and may be used by other projects. The description on its file description page there is shown below.
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}
|
| Date | |
| Source | Own work |
| Author | Shreevatsa |
Licensing
Shreevatsa, the copyright holder of this work, hereby publishes it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
Attribution:
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
This image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
{{vector version available|new image name}}.It is recommended to name the SVG file “Aliquot sums and untouchable numbers.svg”—then the template Vector version available (or Vva) does not need the new image name parameter. |
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26 August 2023
application/pdf
8847bc3f18b9d2705a2976d2a42f261e312a20b8
7,230 byte
1,385 pixel
360 pixel
File history
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| Date/Time | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 04:40, 27 August 2023 | (7 KB) | wikimediacommons>Shreevatsa | Used scalebox to correct for poor rasterization |
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