Sums of proper divisors with missing digits

Let $s(n)$ denote the sum of proper divisors of a positive integer $n$. In 1992, Erdös, Granville, Pomerance, and Spiro conjectured that if $\square$ is a set of integers with asymptotic density zero then the preimage set $s^{−1}(\square)$ also has asymptotic density zero. In this talk, we will discuss the verification of this conjecture when $\square$ is the set of integers with missing digits (also known as ellipsephic integers) by giving a quantitative estimate on the size of the set $s^{-1}(\square)$. This talk is based on the joint work with Giulia Cesana, C\'{e}cile Dartyge, Charlotte Dombrowsky and Lola Thompson.