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Hardy and Littlewood conjectured that every sufficiently large integer iseither a square or the sum of a prime and a square. Let $E(x)$ be the number ofpositive 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 GeneralizedRiemann Hypothesis. This is a small improvement of the previous remarks ofMikawa (1993) and Perelli-Zaccagnini (1995) which claims $A=4,3$ respectively.

A remark on the conditional estimate for the sum of a prime and a square