Investigation of Explicit Formulas for the Difference and Ratio of Sums of Divisors of Perfect Numbers

The paper investigates the properties of the difference and ratio of sums of small and large divisors of even perfect numbers. A new sequence of ratios is discovered, which differs from the known Mersenne numbers. Explicit formulas for these characteristics are derived, and their multiplicative properties are proved. The study reveals a regular structure related to the parameters of a perfect number.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-10-29
DOI
https://doi.org/10.5281/zenodo.23764031
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

Investigation of Explicit Formulas for the Difference and Ratio of Sums of Divisors of Perfect Numbers

Юрий Васильев
4 links
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

Investigation of Explicit Formulas for the Difference and Ratio of Sums of Divisors of Perfect Numbers

Юрий Васильев
preprint en

Abstract

The paper investigates the properties of the difference and ratio of sums of small and large divisors of even perfect numbers. A new sequence of ratios is discovered, which differs from the known Mersenne numbers. Explicit formulas for these characteristics are derived, and their multiplicative properties are proved. The study reveals a regular structure related to the parameters of a perfect number.

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
DOIOpen Access PDFOpenAlex
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Investigation of Explicit Formulas for the Difference and Ratio of Sums of Divisors of Perfect Numbers — Юрий Васильев · Zenodo (CERN European Organization for Nuclear Research) (2026) | TGRS Research Map | TGRS