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 Template:Mvar is an Erdős–Nicolas number when there exists another number Template:Mvar such that

$\sum _{d\mid n,d\le m}d=n.$

The first ten Erdős–Nicolas numbers are

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

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

See also

• Descartes number, another type of almost-perfect numbers