Erdős–Nicolas number

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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

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