Erdős–Nicolas number

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	3304572752464376776401640967110656
OEIS index	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

\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]

References

^ De Koninck, Jean-Marie (2009). Those Fascinating Numbers. American Mathematical Soc. p. 141. ISBN 978-0-8218-4807-4.
^ 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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[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

[1]

[2]

Erdős–Nicolas number

See also

References