In
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 arithmetic function, integer-valued functions. German mathematician Carl Friedrich Gauss (1777â ...
, an Erdős–Nicolas number is a number that is not
perfect, 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
:
The first ten Erdős–Nicolas numbers are
:
24, 2016, 8190, 42336, 45864, 392448, 714240, 1571328, 61900800 and 91963648. ()
They are named after
Paul Erdős
Paul Erdős ( hu, Erdős Pál ; 26 March 1913 – 20 September 1996) was a Hungarian mathematician. He was one of the most prolific mathematicians and producers of mathematical conjectures of the 20th century. pursued and proposed problems in ...
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.
See also
*
Descartes number In number theory, a Descartes number is an odd number which would have been an odd perfect number, if one of its composite factors were prime. They are named after René Descartes who observed that the number would be an odd perfect number if onl ...
, another type of almost-perfect numbers
References
Integer sequences
{{numtheory-stub