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In 1989, E. Saias established an asymptotic formula for $\Psi (x,y)=\left|\left\{n\le x:p\mid n\Rightarrow p\le y\right\}\right|$ with a very good error term, valid for $exp\left({(loglogx)}^{(5/3)+ϵ}\right)\le y\le x$, $x\ge x_0\left(ϵ\right)$, $ϵ\>0.$ We extend this result to an algebraic number field $K$ by obtaining an asymptotic formula for the analogous function ${\Psi }_K(x,y)$ with the same error term and valid in the same region. Our main objective is to compare the formulae for $\Psi (x,y)$ and ${\Psi }_K(x,y),$ and in particular to compare the second term in the two expansions.