On the distribution of square-full integers

Let S(x) be the number of square-full integers not exceeding x and let $$\Delta (x)$$ be the error term in the asymptotic formula for S(x). Under the Riemann hypothesis, we get that $$\Delta (x)\ll x^{\frac{328}{2333}}$$ , which improves the exponent $$\frac{121}{860}$$ obtained by Liu [6].