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. ((sequence A194472 in the OEIS))

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