The reciprocal sum of primitive nondeficient numbers

TL;DR

This paper studies the sum of reciprocals of primitive nondeficient numbers, providing bounds that improve understanding of their distribution and their relation to number density results.

Contribution

The paper establishes new bounds for the reciprocal sum of primitive nondeficient numbers, refining previous knowledge since Erdos's 1934 result.

Findings

Reciprocal sum of pnds is between 0.348 and 0.380

Confirms convergence of the sum as shown by Erdos

Provides tighter bounds on the sum of pnds

Abstract

We investigate the reciprocal sum of primitive nondeficient numbers, or pnds. In 1934, Erdos showed that the reciprocal sum of pnds converges, which he used to prove that the abundant numbers have a natural density. We show the reciprocal sum of pnds is between 0.348 and 0.380.