Question
A number n has this property if for all m less than n, [read slowly] “sigma m over m is less than sigma n over n,” where sigma is the sum-of-divisors function. For 10 points each:
[10h] Name this class of numbers discovered by Leon Alaoglu (“a-la-OH-lu”) and Paul Erdős (“ER-dush”).
ANSWER: superabundant numbers
[10m] If there exists a superabundant number greater than 5,040 that violates Robin’s inequality, that is equivalent to disproving this statement. The generalized form of this statement extends it to all Dirichlet (“DEE-rish-lay”) L-functions.
ANSWER: Riemann hypothesis
[10e] Superabundant numbers were discovered by Alaoglu and Erdős in a work on numbers that are “highly [this property].” This property refers to numbers that are not prime.
ANSWER: composite
<Benjamin McAvoy-Bickford, Other Science>
Summary
| 2024 Penn Bowl CWRU | 11/02/2024 | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2024 Penn Bowl Chicago | 11/02/2024 | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2024 Penn Bowl Texas | 11/02/2024 | Y | 1 | 10.00 | 100% | 0% | 0% |
Data
| Illinois A | WUSTL | 0 | 10 | 10 | 20 |