On the average of the generalized totient function over polynomial sequences (Q1114727)

Let \(\phi\) denote the Euler totient function and let f(x) be an integer coefficient polynomial. \textit{H. N. Shapiro} [Introduction to the theory of numbers (Wiley, New York 1983; Zbl 0515.10001) proved asymptotic formulae for \(\sum_{n\leq x}\phi (f(n))/f(n)\) and \(\sum_{n\leq x}\phi (f(n))\) under certain assumptions on the polynomial f(x). In [Indian J. Pure Appl. Math. 10, 287-302 (1979; Zbl 0393.10003)] the author introduced a generalized Euler totient function over polynomial sequences. In the present paper the author generalizes Shapiro's formulae for that function.