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- W3027420360 abstract "Define s(n) := σ(n) /n (σ(n) = sum of divisors of n) and ω(n) is the number of prime divisors of n. One of the properties of s plays a central role: s(p^a) > s(q^b) if p 0. This result, combined with the Multiplicity Permutation theorem, will help us establish properties of the next counterexample (say c) to Robin's inequality s(n) < e^γ log log n. The number c is superabundant, and ω(c) must be greater than a number close to one billion. In addition, the ratio p_ω(c) / log c has a lower and upper bound. At most ω(c)/14 multiplicity parameters are greater than 1. Last but not least we apply simple methods to sharpen Robin's inequality for various categories of numbers." @default.
- W3027420360 created "2020-05-29" @default.
- W3027420360 creator A5071521776 @default.
- W3027420360 date "2020-05-18" @default.
- W3027420360 modified "2023-09-27" @default.
- W3027420360 title "On numbers satisfying Robin's inequality, properties of the next counterexample and improved specific bounds" @default.
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