Sums of proper divisors with missing digits

Abstract: In 1992, Erdős, Granville, Pomerance, and Spiro conjectured that if $\mathcal{A}$ is a set of integers with asymptotic density zero then the preimage of $\mathcal{A}$ 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 $\mathcal{A}$ 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 $s^{-1}(\mathcal{A})$. This is joint work with Giulia Cesana, Cécile Dartyge, Charlotte Dombrowsky and Lola Thompson.

combinatoricsnumber theory

Audience: researchers in the topic

( paper )

Lethbridge number theory and combinatorics seminar