Erdős–Nicolas number

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

${\displaystyle \sum _{d\mid n,\ d\leq m}d=n.}$^[1]

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

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