Jk. Patel, A LOWER-BOUND TO THE ERROR TERM OF A FUNCTION RELATED TO KTH ORDER FREE INTEGERS (MOD-M), Indian Journal of Pure and Applied Mathematics, 26(1), 1995, pp. 21-27
The multiplicative function g(k)(m(k)) is defined by [GRAPHICS] where
phi is Euler's totient function. It is known that, [GRAPHICS] for a ce
rtain constant C. In this paper, for the corresponding error term, we
show that E(x) = Omega(x(k) log log log x).