Let B( x, y) be the sum taken over all n, 1≤ n≤ x, such that n can be represented as a sum of two squares of integers and n has no prime factors exceeding y. It is shown for u smaller than about .5log log x/log log log x that B( x, x )≈ cxlog xσ( u), where σ( u satisfies a delay differential equation similar to the one satisfied by the Dickman function and c is a positive constant.