Let r1(n) denote the number of representations of the positive integer n as the sum of a square of a positive integer and the square of a positive prime number. We prove an asymptotic evaluation for [sum ]n[les ]xr1(n)2, as x → ∞, thereby improving upon a O-result of Rieger [7]. We further prove an asymptotic formula for the number of positive integers n [les ] x with r1(n) [ges ] 1, which answers a question stated at the end of [7]. Our result in particular shows that for almost all integers represented as the sum of a square and a square of a prime, the representation is unique.