A few weeks ago I found the book "Lure of the Integers" by Joe Roberts, in my schools library, and promptly ordered it from Amazon. It is a wonderful book for those of us who are interested in number theory or numbers in general. The book is a collection of integers with interesting mathematical properties. An example under the integer $10$ is: "The integer $10$ is the only composite integer such that all of its positive integer divisors other than one are of the form $a^r + 1, r > 1$."
While the "Lure of the Integers" contains many obscure and interesting integer properties, it is hardly a comprehensive collection. It may have entries for a few consecutive numbers and then skip the next six. I believe that the author was trying to limit the length of the book by including only the most interesting, obscure, or unusual, results.
Since reading the book, I've been collecting my own list of interesting integer properties.
I was hoping that some of you would share any interesting integer properties that you know of.
Two other examples that I came up with are:
$36$ is the smallest integer expressible as the sum of three distinct non-zero cubes. i.e. $36=1^3+2^3+3^3$
$5$ is the fifth number in both the Fibonacci and Perrin sequences.
I figure I will accept the answer receives the most upvotes.