Erdős–Nicolas number

  • A194472
  • Erdős-Nicolas numbers

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 an Erdős–Nicolas number when there exists another number m such that

∑ d ∣ n ,   d ≤ m d = n . {\displaystyle \sum _{d\mid n,\ d\leq m}d=n.} [1]

The first ten Erdős–Nicolas numbers are

24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, 61900800 and 91963648. (OEIS: A194472)

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

See also

  • Descartes number, another type of almost-perfect numbers

References

  1. ^ De Koninck, Jean-Marie (2009). Those Fascinating Numbers. American Mathematical Soc. p. 141. ISBN 978-0-8218-4807-4.
  2. ^ Erdős, P.; Nicolas, J.L. (1975), "Répartition des nombres superabondants" (PDF), Bull. Soc. Math. France, 79 (103): 65–90, doi:10.24033/bsmf.1793, Zbl 0306.10025
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