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arXiv · 2503.03159

On Robin's Inequality and the Kaneko-Lagarias Inequality

Idris Assani·Aiden Chester·Alex Paschal
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Abstract

We provide new, elementary proofs that Robin's inequality and the Lagarias inequality hold for almost every number, including all numbers not divisible by one of the prime numbers $2$, $3$, $5$; all primorials; given $k$ a natural number, all sufficiently large numbers of the form $2^kn$ for $n\ge1$ odd; and all $21$-free integers. Additionally, we prove that the Kaneko-Lagarias inequality holds for all natural numbers if and only if it holds for all superabundant numbers.

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Idris Assani, Aiden Chester, Alex Paschal. 2025-08-16. On Robin's Inequality and the Kaneko-Lagarias Inequality. https://arxiv.org/abs/2503.03159

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