Some Values of The Function
The first 99 values (sequence A000010 in OEIS) are shown in the table and graph below:
The top line, y = n − 1, is a true upper bound. It is attained whenever n is prime.
The lower line, y ≈ 0.267n which connects the points for n = 30, 60, and 90 is misleading. If the plot were continued, there would be points below it.
(Examples: for n = 210 = 7×30, φ(n) ≈ 0.229 n; for n = 2310 = 11×210 φ(n) ≈ 0.208 n; and for n = 30030 = 13×2310 φ(n) ≈ 0.192 n.)
In fact, there is no lower bound straight line; no matter how gentle the slope of a line (through the origin) is, there will eventually be points of the plot below the line.
Read more about this topic: Euler's Totient Function
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