Buchstab function
The Buchstab function (or Buchstab's function) is the unique continuous function ω : R ≥ 1 → R > 0 {\displaystyle \omega :\mathbb {R} _{\geq 1}\rightarrow \mathbb {R} _{>0}} defined by the delay differential equation ω ( u ) = 1 u , 1 ≤ u ≤ 2 , {\displaystyle \omega (u)={\frac {1}{u}},\qquad \qquad \qquad 1\leq u\leq 2,} d d u ( u ω ( u ) ) = ω ( u − 1 ) , u ≥ 2. {\displaystyle {\frac {d}{du}}(u\omega (u))=\omega (u-1),\qquad u\geq 2.} In the second equation, the derivative at u = 2 should be taken as u approaches 2 from the right.