Sums of Proper Divisors with Missing Digits
Publication date
2024-03-06
Authors
Benli, Kübra
Cesana, Giulia
Dartyge, Cécile
Dombrowsky, Charlotte
Thompson, Lola
Editors
Advisors
Supervisors
Document Type
Part of book
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taverne
Abstract
Let s(n) denote the sum of proper divisors of an integer n. In 1992, Erdős, Granville, Pomerance, and Spiro (EGPS) conjectured that if A is a set of integers with asymptotic density zero, then s−1(A) also has asymptotic density zero. In this chapter we show that the EGPS conjecture holds when A is taken to be a set of integers with missing digits. In particular, we give a sharp upper bound for the size of this preimage set. We also provide an overview of progress toward the EGPS conjecture and survey recent work on sets of integers with missing digits.
Keywords
Taverne, Gender Studies, General Mathematics
Citation
Benli, K, Cesana, G, Dartyge, C, Dombrowsky, C & Thompson, L 2024, Sums of Proper Divisors with Missing Digits. in Women in Numbers Europe IV. Association for Women in Mathematics Series, vol. 32, Springer, pp. 93-110. https://doi.org/10.1007/978-3-031-52163-8_4