A Measure of the Nonmonotonicity of the Euler Phi Function
نویسندگان
چکیده
ure of the nonmonotonicity of f. In particular, F is identically zero if and only if f is strictly increasing . Here we shall take f to be (p, Euler's function, and study the associated function F 4„ which we henceforth call F. We shall show that F(n)/n is asymptotically representable as a function of T(n)/n . Then we shall prove that F(n)/n has a distribution function. We shall study max,,, F(n) and min,,,, F(n) and investigate conditions on (p(n)/n which lead to large and small values of F(n)/n . We express our thanks to Professor Carl Pomerance for a number of helpful comments and suggestions, and to Dr. Charles R. Wall for his unpublished data on the density function of Euler's function .
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