Euler Phi Function/Table
Table of Euler $\phi$ Function
The Euler $\phi$ function for the first $100$ positive integers is as follows:
- $\begin{array} {|r|r|}
\hline n & \map \phi n \\ \hline 1 & 1 \\ 2 & 1 \\ 3 & 2 \\ 4 & 2 \\ 5 & 4 \\ 6 & 2 \\ 7 & 6 \\ 8 & 4 \\ 9 & 6 \\ 10 & 4 \\ 11 & 10 \\ 12 & 4 \\ 13 & 12 \\ 14 & 6 \\ 15 & 8 \\ 16 & 8 \\ 17 & 16 \\ 18 & 6 \\ 19 & 18 \\ 20 & 8 \\ \hline \end{array} \qquad \begin{array} {|r|r|} \hline n & \map \phi n \\ \hline 21 & 12 \\ 22 & 10 \\ 23 & 22 \\ 24 & 8 \\ 25 & 20 \\ 26 & 12 \\ 27 & 18 \\ 28 & 12 \\ 29 & 28 \\ 30 & 8 \\ 31 & 30 \\ 32 & 16 \\ 33 & 20 \\ 34 & 16 \\ 35 & 24 \\ 36 & 12 \\ 37 & 36 \\ 38 & 18 \\ 39 & 24 \\ 40 & 16 \\ \hline \end{array} \qquad \begin{array} {|r|r|} \hline n & \map \phi n \\ \hline 41 & 40 \\ 42 & 12 \\ 43 & 42 \\ 44 & 20 \\ 45 & 24 \\ 46 & 22 \\ 47 & 46 \\ 48 & 16 \\ 49 & 42 \\ 50 & 20 \\ 51 & 32 \\ 52 & 24 \\ 53 & 52 \\ 54 & 18 \\ 55 & 40 \\ 56 & 24 \\ 57 & 36 \\ 58 & 28 \\ 59 & 58 \\ 60 & 16 \\ \hline \end{array} \qquad \begin{array} {|r|r|} \hline n & \map \phi n \\ \hline 61 & 60 \\ 62 & 30 \\ 63 & 36 \\ 64 & 32 \\ 65 & 48 \\ 66 & 20 \\ 67 & 66 \\ 68 & 32 \\ 69 & 44 \\ 70 & 24 \\ 71 & 70 \\ 72 & 24 \\ 73 & 72 \\ 74 & 36 \\ 75 & 40 \\ 76 & 36 \\ 77 & 60 \\ 78 & 24 \\ 79 & 78 \\ 80 & 32 \\ \hline \end{array} \qquad \begin{array} {|r|r|} \hline n & \map \phi n \\ \hline 81 & 54 \\ 82 & 40 \\ 83 & 82 \\ 84 & 24 \\ 85 & 64 \\ 86 & 42 \\ 87 & 56 \\ 88 & 40 \\ 89 & 88 \\ 90 & 24 \\ 91 & 72 \\ 92 & 44 \\ 93 & 60 \\ 94 & 46 \\ 95 & 72 \\ 96 & 32 \\ 97 & 96 \\ 98 & 42 \\ 99 & 60 \\ 100 & 40 \\ \hline \end{array}$
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 $\map \sigma n$