Lethbridge Number Theory and Combinatorics Seminar: Kübra Benli

In 1992, Erd˝os, Granville, Pomerance, and Spiro conjectured that if A is a set of integers with asymptotic density zero then the preimage of A under s(n), sum-of-proper-divisors function, also has asymptotic density zero. In this talk, we will discuss the verification of this conjecture when A is taken to be the set of integers with missing digits (also known as ellipsephic integers) by giving a quantitative estimate on the size of the set s−1(A). This is joint work with Giulia Cesana, C´ecile Dartyge, Charlotte Dombrowsky and Lola Thompson.