{
  "abstract": "In this article, we establish four lower-bound inequalities for rational expressions involving the Euler totient function φ(n), the Dedekind psi function ψ(n), and the sum-of-divisors function σ(n). The inequalities concern rational expressions involving sums of cubes, products of these arithmetic functions, and sums of pairs of these functions. The lower bounds are given explicitly as rational functions of n and are attained when n is prime. Furthermore, we formulate four conjectures that extend the established inequalities to arbitrary positive integer powers k.",
  "abstract_shown": true,
  "affiliations": [
    "Department of Mathematical Analysis and Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, Blvd. St. Kliment Ohridski 8, 1000 Sofia, Bulgaria",
    "Department of Mathematical Modelling and Numerical Methods, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 8 “Kliment Ohridski” Blvd., 1000 Sofia, Bulgaria",
    "Department of Mathematics, Informatics and Physics, Prof. Dr. Assen Zlatarov State University of Burgas, 1 Prof. Yakimov Blvd., 8000 Burgas, Bulgaria"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 2,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Stoyan Dimitrov",
      "orcid": "0000-0002-5265-0289"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Meglena Lazarova"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4g0m02wq0t4f.bib",
  "cited_by": 0,
  "doi": "10.3390/math14213935",
  "fulltext_url": null,
  "id": "e4g0m02wq0t4f",
  "issns": [
    "2227-7390"
  ],
  "landing_url": "https://www.mdpi.com/2227-7390/14/21/3935",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7224106361",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": "MDPI AG",
  "ris": "https://research.draconitic.com/paper/e4g0m02wq0t4f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:29Z",
      "native_id": "10.3390/math14213935",
      "source": "crossref",
      "url": "https://www.mdpi.com/2227-7390/14/21/3935"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2602|Analytic Number Theory Research",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lower Bounds on Expressions Depending on the Functions φ(n), ψ(n) and σ(n): Part 4",
  "title_text": "Lower Bounds on Expressions Depending on the Functions φ(n), ψ(n) and σ(n): Part 4",
  "type": "peer-reviewed",
  "updated_at": "2026-10-30T12:18:29Z",
  "url": "https://research.draconitic.com/paper/e4g0m02wq0t4f",
  "venue": "Mathematics",
  "versions": []
}