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	1371332329173024768
OEIS index	A194472

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

$\sum_{d\mid n,\ d\leq m}d=n.$

The first ten Erdős–Nicolas numbers are

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

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