PreprintCC BY 4.0arXiv
Strongly Pseudoperfect Numbers
Abstract
A positive integer n is said to be strongly pseudoperfect if there is a subset S of the positive divisors of n such that d ∈ S if and only if n/d ∈ S, and ∑d ∈ S d = 2n. We construct new infinite families of strongly pseudoperfect numbers, and also prove new restrictions on when a positive integer n can be strongly pseudoperfect.
Related
BibTeX
@misc{wang2026strongly,
title = {{Strongly Pseudoperfect Numbers}},
author = {Audrey Wang and Joshua Zelinsky},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.36068},
eprint = {2609.36068},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.36068},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Strongly Pseudoperfect Numbers
AU - Audrey Wang
AU - Joshua Zelinsky
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2609.36068
UR - https://arxiv.org/abs/2609.36068
AB - A positive integer n is said to be strongly pseudoperfect if there is a subset S of the positive divisors of n such that d ∈ S if and only if n/d ∈ S, and ∑_d ∈ S d = 2n. We construct new infinite families of strongly pseudoperfect numbers, and also prove new restrictions on when a positive integer n can be strongly pseudoperfect.
ER -