Erdős–Nicolas number

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Erdős–Nicolas number
Named after Paul Erdős, Jean-Louis Nicolas
Publication year 1975
Author of publication Erdős, P., Nicolas, J. L.
Subsequence of Abundant numbers
First terms 24, 2016, 8190
Largest known term 1371332329173024768
OEIS index

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


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 also[edit]


  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