Divisor Count Function/Table

== Table of Divisor Count Function ==
The divisor count function for the first $200$ positive integers is as follows:
$\quad \begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
1 & 1 \\
2 & 2 \\
3 & 2 \\
4 & 3 \\
5 & 2 \\
6 & 4 \\
7 & 2 \\
8 & 4 \\
9 & 3 \\
10 & 4 \\
11 & 2 \\
12 & 6 \\
13 & 2 \\
14 & 4 \\
15 & 4 \\
16 & 5 \\
17 & 2 \\
18 & 6 \\
19 & 2 \\
20 & 6 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
21 & 4 \\
22 & 4 \\
23 & 2 \\
24 & 8 \\
25 & 3 \\
26 & 4 \\
27 & 4 \\
28 & 6 \\
29 & 2 \\
30 & 8 \\
31 & 2 \\
32 & 6 \\
33 & 4 \\
34 & 4 \\
35 & 4 \\
36 & 9 \\
37 & 2 \\
38 & 4 \\
39 & 4 \\
40 & 8 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
41 & 2 \\
42 & 8 \\
43 & 2 \\
44 & 6 \\
45 & 6 \\
46 & 4 \\
47 & 2 \\
48 & 10 \\
49 & 3 \\
50 & 6 \\
51 & 4 \\
52 & 6 \\
53 & 2 \\
54 & 8 \\
55 & 4 \\
56 & 8 \\
57 & 4 \\
58 & 4 \\
59 & 2 \\
60 & 12 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
61 & 2 \\
62 & 4 \\
63 & 6 \\
64 & 7 \\
65 & 4 \\
66 & 8 \\
67 & 2 \\
68 & 6 \\
69 & 4 \\
70 & 8 \\
71 & 2 \\
72 & 12 \\
73 & 2 \\
74 & 4 \\
75 & 6 \\
76 & 6 \\
77 & 4 \\
78 & 8 \\
79 & 2 \\
80 & 10 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
81 & 5 \\
82 & 4 \\
83 & 2 \\
84 & 12 \\
85 & 4 \\
86 & 4 \\
87 & 4 \\
88 & 8 \\
89 & 2 \\
90 & 12 \\
91 & 4 \\
92 & 6 \\
93 & 4 \\
94 & 4 \\
95 & 4 \\
96 & 12 \\
97 & 2 \\
98 & 6 \\
99 & 6 \\
100 & 9 \\
\hline
\end{array}$
$\quad \begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
101 & 2 \\
102 & 8 \\
103 & 2 \\
104 & 8 \\
105 & 8 \\
106 & 4 \\
107 & 2 \\
108 & 12 \\
109 & 2 \\
110 & 8 \\
111 & 4 \\
112 & 10 \\
113 & 2 \\
114 & 8 \\
115 & 4 \\
116 & 6 \\
117 & 6 \\
118 & 4 \\
119 & 4 \\
120 & 16 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
121 & 3 \\
122 & 4 \\
123 & 4 \\
124 & 6 \\
125 & 4 \\
126 & 12 \\
127 & 2 \\
128 & 8 \\
129 & 4 \\
130 & 8 \\
131 & 2 \\
132 & 12 \\
133 & 4 \\
134 & 4 \\
135 & 8 \\
136 & 8 \\
137 & 2 \\
138 & 8 \\
139 & 2 \\
140 & 12 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
141 & 4 \\
142 & 4 \\
143 & 4 \\
144 & 15 \\
145 & 4 \\
146 & 4 \\
147 & 6 \\
148 & 6 \\
149 & 2 \\
150 & 12 \\
151 & 2 \\
152 & 8 \\
153 & 6 \\
154 & 8 \\
155 & 4 \\
156 & 12 \\
157 & 2 \\
158 & 4 \\
159 & 4 \\
160 & 12 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
161 & 4 \\
162 & 10 \\
163 & 2 \\
164 & 6 \\
165 & 8 \\
166 & 4 \\
167 & 2 \\
168 & 16 \\
169 & 3 \\
170 & 8 \\
171 & 6 \\
172 & 6 \\
173 & 2 \\
174 & 8 \\
175 & 6 \\
176 & 10 \\
177 & 4 \\
178 & 4 \\
179 & 2 \\
180 & 18 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map {\sigma_0} n \\
\hline
181 & 2 \\
182 & 8 \\
183 & 4 \\
184 & 8 \\
185 & 4 \\
186 & 8 \\
187 & 4 \\
188 & 6 \\
189 & 8 \\
190 & 8 \\
191 & 2 \\
192 & 14 \\
193 & 2 \\
194 & 4 \\
195 & 8 \\
196 & 9 \\
197 & 2 \\
198 & 12 \\
199 & 2 \\
200 & 12 \\
\hline
\end{array}$
== Sources ==
* : $\text {3-5}$ The Use of Computers in Number Theory: Exercise $1$
* : Tables: $8$ The Proper Factors, where Composite, and the Values of the Functions $\map \phi n$, $\map d n$ and $\map \sigma n$
* : 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 Count Function