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SUMMARY:Unsinkable numbers [MPIM]
DTSTART:20260716T143000Z
DTEND:20260716T160000Z
DTSTAMP:20260913T021600Z
UID:indico-event-1497@math-events.uni-bonn.de
DESCRIPTION:Speakers: Lola Thompson (Utrecht University)\n\nNumber theory 
 lunch seminar \nLet s(n) denote the sum of proper divisors of an integer 
 n. In honour of the Number Theory Boat Seminar\, we coin the term "unsinka
 ble numbers" for integers n whose sequence of iterates under s never event
 ually "sinks" to 1. We will give an overview of what is known about unsink
 able numbers as well as some open conjectures.\nWe will then turn to a dif
 ferent aspect of the sum-of-proper-divisors function: the distribution of 
 the digits of s(n). We will see that s(n) obeys Benford's law and that\, a
 symptotically\, almost every value of s(n) contains every decimal digit am
 ong both its leading and trailing k(x) digits\, where k(x)→∞. We will 
 also discuss recent work showing that values of s(n) missing a decimal dig
 it are surprisingly rare\, with prime inputs providing the main contributi
 on\, confirming a special case of a conjecture of Erdős\, Granville\, Pom
 erance\, and Spiro.\nThis talk is based on joint work with various subsets
  of the following co-authors: Kübra Benli\, Giulia Cesana\, Cécile Darty
 ge\, Charlotte Dombrowsky\, and Paul Pollack.\n\nhttps://math-events.uni-b
 onn.de/event/1497/
LOCATION:MPIM\, Vivatsgasse\,  7 - Seminar Room (Max Planck Institute for 
 Mathematics)
URL:https://math-events.uni-bonn.de/event/1497/
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