Closely related delay differential equations appeared in the 30s and 40s in the completely different settings. K. Dickman studied the statistics of integers with the "small" prime factors, and. V. Goncharov in his fundamental paper from 1944 investigated the distribution of the length of the cycles in the random permutation, i.e., an element of S_n. The connection between these equations was discovered by A. Vershik in the 60s. He with the collaborators proved several new results on the random permutations. In 2004-2010 M. Penrose and A. Wade published a series of papers on the application (of what they called the Dickman distribution) to the theory of the random graphs.  The talk will contain a review (in some cases almost detective) of this topic, which popular is in the applied mathematics. Based on the paper by S. Molchanov and  V. Panov, Russian Math Surveys, 2021. The references to this paper contain more than 60 recent publications.