Pith. sign in

REVIEW

On Near Perfect Numbers

Not yet reviewed by Pith; the record is open.

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 1610.04253 v4 pith:UJFZWG7Q submitted 2016-10-13 math.NT

On Near Perfect Numbers

classification math.NT
keywords numbersdivisorsnumberperfectpropersomeantiquityasymptotic
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

The study of perfect numbers (numbers which equal the sum of their proper divisors) goes back to antiquity, and is responsible for some of the oldest and most popular conjectures in number theory. We investigate a generalization introduced by Pollack and Shevelev: $k$-near-perfect numbers. These are examples to the well-known pseudoperfect numbers first defined by Sierpi\'nski, and are numbers such that the sum of all but at most $k$ of its proper divisors equals the number. We establish their asymptotic order for all integers $k\ge 4$, as well as some properties of related quantities.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.