{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2007:ZRB2XOG5EAIDYHJX6HDANNQ43A","short_pith_number":"pith:ZRB2XOG5","schema_version":"1.0","canonical_sha256":"cc43abb8dd20103c1d37f1c606b61cd83e95827ae69f4e34fdd72fb3852c723d","source":{"kind":"arxiv","id":"0710.2424","version":1},"attestation_state":"computed","paper":{"title":"The Nicolas and Robin inequalities with sums of two squares","license":"","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"C. Wesley Nevans, Derrick N. Hart, Pieter Moree, William D. Banks","submitted_at":"2007-10-12T10:20:01Z","abstract_excerpt":"In 1984, G. Robin proved that the Riemann hypothesis is true if and only if the Robin inequality $\\sigma(n)5040$, where $\\sigma(n)$ is the sum of divisors function, and $\\gamma$ is the Euler-Mascheroni constant. We exhibit a broad class of subsets $\\cS$ of the natural numbers such that the Robin inequality holds for all but finitely many $n\\in\\cS$. As a special case, we determine the finitely many numbers of the form $n=a^2+b^2$ that do not satisfy the Robin inequality. In fact, we prove our assertions with the Nicolas inequality $n/\\phi(n)5040$, where $\\sigma(n)$ is the sum of divisors function, and $\\gamma$ is the Euler-Mascheroni constant. We exhibit a broad class of subsets $\\cS$ of the natural numbers such that the Robin inequality holds for all but finitely many $n\\in\\cS$. As a special case, we determine the finitely many numbers of the form $n=a^2+b^2$ that do not satisfy the Robin inequality. In fact, we prove our assertions with the Nicolas inequality $n/\\phi(n)