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Let $\{Z_k\}_{k\geqslant 1}$ denote a sequence of independent Bernoullirandom variables defined by ${\mathbb P}(Z_k=1)=1/k=1-{\mathbb P}(Z_k=0)$$(k\geqslant 1)$ and put $T_n:=\sum_{1\leqslant k\leqslant n}kZ_k$. It is thenknown that $T_n/n$ converges weakly to a real random variable $D$ with densityproportional to the Dickman function, defined by the delay-differentialequation $u\varrho'(u)+\varrho(u-1)=0$ $(u>1)$ with initial condition$\varrho(u)=1$ $(0\leqslant u\leqslant 1)$. Improving on earlier work, wepropose asymptotic formulae with remainders for the corresponding local andalmost sure limit theorems.

On strong and almost sure local limit theorems for a probabilistic model of the Dickman distribution