A Generalization of the Sum of Divisors Function

Darrell Cox; Sourangshu Ghosh; Eldar Sultanow

doi:10.20944/preprints202203.0025.v3

Preprint Article Version 3 Preserved in Portico This version is not peer-reviewed

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)

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).

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

Computer Science and Mathematics, Algebra and Number Theory

Comment 1

Received: 7 March 2022
Commenter: Darrell Cox
Commenter's Conflict of Interests: Author

Comment: Deleted dubious material on spectra. The article is more concise and there are fewer images.

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A Generalization of the Sum of Divisors Function

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