Dickman–de Bruijn function
From specialfunctionswiki
The Dickman–de Bruijn function $\rho(u)$ solves the initial value problem $$up'(u)+p(u-1)=0$$ where $p(u)=1$ for $0 \leq u \leq 1$.
References
On sums involving reciprocals of the largest prime factor of an integer
