number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

, an Erdős–Nicolas number is a number that is not

perfect Perfect commonly refers to: * Perfection, completeness, excellence * Perfect (grammar), a grammatical category in some languages Perfect may also refer to: Film * Perfect (1985 film), ''Perfect'' (1985 film), a romantic drama * Perfect (2018 f ...

, but that equals one of the

partial sum In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, math ...

s of its

divisor In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible or evenly divisible by ...

s. That is, a number is Erdős–Nicolas number when there exists another number such that :

\sum_d=n.

The first ten Erdős–Nicolas numbers are : 24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, 61900800 and 91963648. () They are named after Paul Erdős and

Jean-Louis Nicolas Jean-Louis Nicolas is a French number theorist. He is the namesake (with Paul Erdős) of the Erdős–Nicolas numbers, and was a frequent co-author of Erdős, who would take over the desk of Nicolas' wife Anne-Marie (also a mathematician) whenev ...

, who wrote about them in 1975.

References

Integer sequences {{numtheory-stub

See also

References