Primary Pseudoperfect Numbers, Arithmetic Progressions, and the Erdos-Moser Equation

摘要

A primary pseudoperfect number (PPN) is an integer K > 1 such that the reciprocals of K and its prime factors sum to 1. PPNs arise in studying perfectly weighted graphs and singularities of algebraic surfaces, and are related to Sylvester's sequence, Giuga numbers, Zn ' am's problem, and Curtiss's bound on solutions of a unit fraction equation.