Erdős–Nicolas number

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Erdős–Nicolas number
Named afterPaul Erdős, Jean-Louis Nicolas
Publication year1975
Author of publicationErdős, P., Nicolas, J. L.
Subsequence ofAbundant numbers
First terms24, 2016, 8190
Largest known term3304572752464376776401640967110656
OEIS index

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

[math]\displaystyle{ \sum_{d\mid n,\ d\leq m}d=n. }[/math][1]

The first ten Erdős–Nicolas numbers are

24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, 61900800 and 91963648. (OEISA194472)

They are named after Paul Erdős and Jean-Louis Nicolas, who wrote about them in 1975.[2]

See also