On 2-Near Perfect Numbers
Vedant Aryan, Dev Madhavani, Savan Parikh, Ingrid Slattery, Joshua, Zelinsky

TL;DR
This paper characterizes 2-near perfect numbers, especially those of the form 2^k p^i, and explores related divisor sum properties, expanding understanding of near perfect number classifications.
Contribution
It provides a complete description of 2-near perfect numbers of specific forms and proves new results under divisor product restrictions.
Findings
Characterization of 2-near perfect numbers of the form 2^k p^i
Complete classification for these forms
Results under the condition d_1 d_2 = n
Abstract
Let be the sum of the positive divisors of . A number is said to be 2-near perfect if , where and are distinct positive divisors of . We give a complete description of those which are 2-near perfect and of the form where is prime and . We also prove related results under the additional restriction where .
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Taxonomy
TopicsAdvanced Mathematical Theories · Analytic Number Theory Research
