Erdős–Nicolas number

In number theory, an Erdős–Nicolas number is a number that is not perfect, but that equals one of the partial sums of its divisors. That is, a number n is Erdős–Nicolas number when there exists another number m such that

Erdős–Nicolas number
Named afterPaul Erdős, Jean-Louis Nicolas
Publication year1975
Author of publicationErdős, P., Nicolas, J. L.
Subsequence ofAbundant numbers
First terms24, 2016, 8190
Largest known term1371332329173024768
OEIS index

The first ten Erdős–Nicolas numbers are

24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, 61900800 and 91963648. (OEISA194472)

They are named after Paul Erdős and Jean-Louis Nicolas, who wrote about them in 1975.[2]

See alsoEdit


  1. ^ De Koninck, Jean-Marie (2009). Those Fascinating Numbers. p. 141. ISBN 978-0-8218-4807-4.
  2. ^ Erdős, P.; Nicolas, J.L. (1975), "Répartition des nombres superabondants" (PDF), Bull. Soc. Math. France (103): 65–90, Zbl 0306.10025