Buchstab function

The Buchstab function is a continuous function $\omega \colon [1,\infty) \rightarrow (0,\infty)$ defined by the initial value problem $$\dfrac{\mathrm{d}}{\mathrm{d}u}\Big(u\omega(u-1)\Big); u \geq 2$$ and for $1 \leq u \leq 2$, $\omega(u)=\dfrac{1}{u}$.

References

A differential delay equation arising from the Sieve of Eratosthenes