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Article
Some Conjectures on the Divisor Function
Author(s)
Masatoshi Nakano
Full-Text PDF XML 1430 Views
DOI:10.17265/2159-5291/2020.02.002
Affiliation(s)
Kesennuma College of Technology, 1-174 Ohtougeyama Kesennuma-shi, Miyagi 988-0812, Japan
ABSTRACT
We propose the following conjecture onthe sum-of-divisors function:will increase strictly and converge to when n runs from the colossally abundant numbers to infinity This conjecture is a sufficient condition for
the and converge to whenruns
from the colossally abundant numbers to infinity. This
conjecture is a sufficient condition for the Riemann
hypothesis by Robin’s
theorem, and it is confirmed for n from up to 10103078. Further, we present two additional Riemann
hypothesis by Robin’s
theorem, and it is confirmed for from up to 10103078. Further, we present two additional conjectures that are related to Robin’s
theorem.
KEYWORDS
Riemann hypothesis, Robin’s theorem, colossally abundant number, divisor function.
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