dickman_rho( z )

The Dickman function of z in SageMath. The solution to the differential equation

$x \rho' (x) + \rho (x-1) = 0$

with initial condition $$\rho (x) = 1$$ for $$0 \le x \le 1$$.

Plot on the real axis:

Semilog plot on the real axis: