The arithmetic function whose value at is equal to the number of positive integers not exceeding and relatively prime to . The Euler function is multiplicative, that is and for . The function satisfies the relations
It was introduced by L. Euler (1763).
|||K. Chandrasekharan, "Introduction to analytic number theory" , Springer (1968)|
The function can be evaluated by , where the product is taken over all primes dividing , cf. [a1].
For a derivation of the asymptotic formula in the article above, as well as of the formula
|[a1]||G.H. Hardy, E.M. Wright, "An introduction to the theory of numbers" , Oxford Univ. Press (1979) pp. Chapts. 5; 7; 8|
Euler function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Euler_function&oldid=11814