Journal of Integer Sequences, Vol. 29 (2026), Article 26.1.3

The Reciprocal Sum of Even Pseudoprimes


Xuyan Cheng
Department of Computer Science and Engineering
The Ohio State University
Columbus, OH 43201
USA

Paul Kinlaw
College of Arts and Sciences
The University of Maine at Presque Isle
Presque Isle, ME 04769
USA

Duc Nguyen
Department of Mathematics
Dickinson College
28N College St.
Carlisle, PA 17013
USA

Abstract:

A pseudoprime is a composite integer that mimics the behavior of primes by satisfying the congruence 2N ≡ 2 (mod N) in Fermat's little theorem. This paper focuses on the subset of even pseudoprimes and obtains an upper bound for the sum of their reciprocals. Our approach combines analytic arguments with computational verification, showing that this sum is less than 0.0059.

Full version:  pdf,    dvi,    ps,    latex    

(Concerned with sequences A006935.)

Received October 24 2024; revised version received October 25 2024; November 4 2025; December 19 2025. Published in Journal of Integer Sequences, January 26 2026.

Return to Journal of Integer Sequences home page