Divisor Sum Function/Table

== Table of Divisor Sum Function ==
The divisor sum function for the first $200$ positive integers is as follows:
$\quad \begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
1 & 1 \\
2 & 3 \\
3 & 4 \\
4 & 7 \\
5 & 6 \\
6 & 12 \\
7 & 8 \\
8 & 15 \\
9 & 13 \\
10 & 18 \\
11 & 12 \\
12 & 28 \\
13 & 14 \\
14 & 24 \\
15 & 24 \\
16 & 31 \\
17 & 18 \\
18 & 39 \\
19 & 20 \\
20 & 42 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
21 & 32 \\
22 & 36 \\
23 & 24 \\
24 & 60 \\
25 & 31 \\
26 & 42 \\
27 & 40 \\
28 & 56 \\
29 & 30 \\
30 & 72 \\
31 & 32 \\
32 & 63 \\
33 & 48 \\
34 & 54 \\
35 & 48 \\
36 & 91 \\
37 & 38 \\
38 & 60 \\
39 & 56 \\
40 & 90 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
41 & 42 \\
42 & 96 \\
43 & 44 \\
44 & 84 \\
45 & 78 \\
46 & 72 \\
47 & 48 \\
48 & 124 \\
49 & 57 \\
50 & 93 \\
51 & 72 \\
52 & 98 \\
53 & 54 \\
54 & 120 \\
55 & 72 \\
56 & 120 \\
57 & 80 \\
58 & 90 \\
59 & 60 \\
60 & 168 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
61 & 62 \\
62 & 96 \\
63 & 104 \\
64 & 127 \\
65 & 84 \\
66 & 144 \\
67 & 68 \\
68 & 126 \\
69 & 96 \\
70 & 144 \\
71 & 72 \\
72 & 195 \\
73 & 74 \\
74 & 114 \\
75 & 124 \\
76 & 140 \\
77 & 96 \\
78 & 168 \\
79 & 80 \\
80 & 186 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
81 & 121 \\
82 & 126 \\
83 & 84 \\
84 & 224 \\
85 & 108 \\
86 & 132 \\
87 & 120 \\
88 & 180 \\
89 & 90 \\
90 & 234 \\
91 & 112 \\
92 & 168 \\
93 & 128 \\
94 & 144 \\
95 & 120 \\
96 & 252 \\
97 & 98 \\
98 & 171 \\
99 & 156 \\
100 & 217 \\
\hline
\end{array}$
$\quad \begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
101 & 102 \\
102 & 216 \\
103 & 104 \\
104 & 210 \\
105 & 192 \\
106 & 162 \\
107 & 108 \\
108 & 280 \\
109 & 110 \\
110 & 216 \\
111 & 152 \\
112 & 248 \\
113 & 114 \\
114 & 240 \\
115 & 144 \\
116 & 210 \\
117 & 182 \\
118 & 180 \\
119 & 144 \\
120 & 360 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
121 & 133 \\
122 & 186 \\
123 & 168 \\
124 & 224 \\
125 & 156 \\
126 & 312 \\
127 & 128 \\
128 & 255 \\
129 & 176 \\
130 & 252 \\
131 & 132 \\
132 & 336 \\
133 & 160 \\
134 & 204 \\
135 & 240 \\
136 & 270 \\
137 & 138 \\
138 & 288 \\
139 & 140 \\
140 & 336 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
141 & 192 \\
142 & 216 \\
143 & 168 \\
144 & 403 \\
145 & 180 \\
146 & 222 \\
147 & 228 \\
148 & 266 \\
149 & 150 \\
150 & 372 \\
151 & 152 \\
152 & 300 \\
153 & 234 \\
154 & 288 \\
155 & 192 \\
156 & 392 \\
157 & 158 \\
158 & 240 \\
159 & 216 \\
160 & 378 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
161 & 192 \\
162 & 363 \\
163 & 164 \\
164 & 294 \\
165 & 288 \\
166 & 252 \\
167 & 168 \\
168 & 480 \\
169 & 183 \\
170 & 324 \\
171 & 260 \\
172 & 308 \\
173 & 174 \\
174 & 360 \\
175 & 248 \\
176 & 372 \\
177 & 240 \\
178 & 270 \\
179 & 180 \\
180 & 546 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_1} n \\
\hline
181 & 182 \\
182 & 336 \\
183 & 248 \\
184 & 360 \\
185 & 228 \\
186 & 384 \\
187 & 216 \\
188 & 336 \\
189 & 320 \\
190 & 360 \\
191 & 192 \\
192 & 508 \\
193 & 194 \\
194 & 294 \\
195 & 336 \\
196 & 399 \\
197 & 198 \\
198 & 468 \\
199 & 200 \\
200 & 465 \\
\hline
\end{array}$
== Sources ==
* : $\text {3-5}$ The Use of Computers in Number Theory: Exercise $10$
* : Tables: $8$ The Proper Factors, where Composite, and the Values of the Functions $\map \phi n$, $\map d n$ and $\map \sigma n$
* : Chapter $\text {B}.2$: More about Numbers: Irrationals, Perfect Numbers and Mersenne Primes
* : Tables: $8$ The Proper Factors, where Composite, and the Values of the Functions $\map \phi n$, $\map d n$ and $\map \sigma n$
Category:Examples of Divisor Sum Function