Abstract. In this talk I will discuss two different topics. The first one deals with a problem of Chen and Liu on the distribution of subsequences of e_p(n!) in residue classes, where e_p(n!) denotes the order of a fixed prime p in the prime factorization of n!. In the second part of the talk I will study a reverse order property of the sum-of-digits function related to a question of Thomas Cusick. For an integer t let t^R be the integer obtained from t by reversing the order of the digits of the representation in base q. I will discuss a relation between s_q(n+t) and s_q(n+t^R), where s_q denotes the sum-of-digits function in base q. The first part is joint work with Thomas Stoll and the second part with Lukas Spiegelhofer.