  Hardy and Littlewood conjectured that every sufficiently large integer is
either a square or the sum of a prime and a square. Let $E(x)$ be the number of
positive integers up to $x\ge4$ which does not satisfy this condition. We prove
$E(x)\ll x^{1/2}(\log x)^A(\log\log x)^4$with $A=3/2$ under the Generalized
Riemann Hypothesis. This is a small improvement of the previous remarks of
Mikawa (1993) and Perelli-Zaccagnini (1995) which claims $A=4,3$ respectively.
