Euler Phi Function/Table
Table of Euler $\phi$ Function
The Euler $\phi$ function for the first $100$ positive integers is as follows:
$\quad \begin{array} {|r|r|}
\hline
n & \map \phi n \\
\hline
1 & 1 \\
2 & 1 \\
3 & 2 \\
4 & 2 \\
5 & 4 \\
6 & 2 \\
7 & 6 \\
8 & 4 \\
9 & 6 \\
10 & 4 \\
11 & 10 \\
12 & 4 \\
13 & 12 \\
14 & 6 \\
15 & 8 \\
16 & 8 \\
17 & 16 \\
18 & 6 \\
19 & 18 \\
20 & 8 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map \phi n \\
\hline
21 & 12 \\
22 & 10 \\
23 & 22 \\
24 & 8 \\
25 & 20 \\
26 & 12 \\
27 & 18 \\
28 & 12 \\
29 & 28 \\
30 & 8 \\
31 & 30 \\
32 & 16 \\
33 & 20 \\
34 & 16 \\
35 & 24 \\
36 & 12 \\
37 & 36 \\
38 & 18 \\
39 & 24 \\
40 & 16 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map \phi n \\
\hline
41 & 40 \\
42 & 12 \\
43 & 42 \\
44 & 20 \\
45 & 24 \\
46 & 22 \\
47 & 46 \\
48 & 16 \\
49 & 42 \\
50 & 20 \\
51 & 32 \\
52 & 24 \\
53 & 52 \\
54 & 18 \\
55 & 40 \\
56 & 24 \\
57 & 36 \\
58 & 28 \\
59 & 58 \\
60 & 16 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map \phi n \\
\hline
61 & 60 \\
62 & 30 \\
63 & 36 \\
64 & 32 \\
65 & 48 \\
66 & 20 \\
67 & 66 \\
68 & 32 \\
69 & 44 \\
70 & 24 \\
71 & 70 \\
72 & 24 \\
73 & 72 \\
74 & 36 \\
75 & 40 \\
76 & 36 \\
77 & 60 \\
78 & 24 \\
79 & 78 \\
80 & 32 \\
\hline
\end{array} \qquad
\begin{array} {|r|r|}
\hline
n & \map \phi n \\
\hline
81 & 54 \\
82 & 40 \\
83 & 82 \\
84 & 24 \\
85 & 64 \\
86 & 42 \\
87 & 56 \\
88 & 40 \\
89 & 88 \\
90 & 24 \\
91 & 72 \\
92 & 44 \\
93 & 60 \\
94 & 46 \\
95 & 72 \\
96 & 32 \\
97 & 96 \\
98 & 42 \\
99 & 60 \\
100 & 40 \\
\hline
\end{array}$
This sequence is A000010 in the On-Line Encyclopedia of Integer Sequences (N. J. A. Sloane (Ed.), 2008).
Sources
- 1971: George E. Andrews: Number Theory ... (previous) ... (next): $\text {3-5}$ The Use of Computers in Number Theory: Exercise $11$
- 1986: David Wells: Curious and Interesting Numbers ... (previous) ... (next): Tables: $8$ The Proper Factors, where Composite, and the Values of the Functions $\map \phi n$, $\map d n$ and $\map \sigma n$
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): Tables: $8$ The Proper Factors, where Composite, and the Values of the Functions $\map \phi n$, $\map d n$ and $\map \sigma n$