Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

A Generalization of the Sum of Divisors Function

Version 1 : Received: 26 February 2022 / Approved: 1 March 2022 / Online: 1 March 2022 (14:43:37 CET)
Version 2 : Received: 3 March 2022 / Approved: 3 March 2022 / Online: 3 March 2022 (10:14:28 CET)
Version 3 : Received: 6 March 2022 / Approved: 7 March 2022 / Online: 7 March 2022 (10:53:32 CET)
Version 4 : Received: 16 March 2022 / Approved: 17 March 2022 / Online: 17 March 2022 (11:57:24 CET)
Version 5 : Received: 17 March 2022 / Approved: 18 March 2022 / Online: 18 March 2022 (12:11:02 CET)
Version 6 : Received: 24 March 2022 / Approved: 25 March 2022 / Online: 25 March 2022 (10:05:06 CET)

How to cite: Cox, D.; Ghosh, S.; Sultanow, E. A Generalization of the Sum of Divisors Function. Preprints 2022, 2022030025 (doi: 10.20944/preprints202203.0025.v2). Cox, D.; Ghosh, S.; Sultanow, E. A Generalization of the Sum of Divisors Function. Preprints 2022, 2022030025 (doi: 10.20944/preprints202203.0025.v2).

Abstract

A generalization of the sum of divisors function involves a recursive definition. This leads to variants of superabundant numbers, colossally abundant numbers, and Gronwall's theorem (relevant to the Riemann hypothesis).

Keywords

sum of divisors function; superabundant numbers; colossally abundant numbers; Riemann hypothesis

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comments (1)

Comment 1
Received: 3 March 2022
Commenter: Darrell Cox
Commenter's Conflict of Interests: Author
Comment: More empirical evidence has been collected.
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