On the number of y-smooth natural numbers ≤x representable as a sum of two integer squares

LetB(x,y) be the sum taken over alln, 1≤n≤x, such that n can be represented as a sum of two squares of integers andn has no prime factors exceedingy. It is shown foru smaller than about .5log logx/log log logx thatB(x,x ^1/u)≈cxlog^-1/2 xσ(u), where σ(u satisfies a delay differential equation similar to the one satisfied by the Dickman function andc is a positive constant.