It is a happy number.
The square root of 4096 is 64.
The cubic root of 4096 is 16.
It is a Jordan-Polya number, since it can be written as (2!)12.
4096 is nontrivially palindromic in base 7 and base 15.
It is a Duffinian number.
It is a nialpdrome in base 2, base 4, base 8, base 9 and base 16.
In principle, a polygon with 4096 sides can be constructed with ruler and compass.
It is an impolite number, since it cannot be written as a nontrivial sum of consecutive naturals.
4096 is a Friedman number, since it can be written as (9-6^0)^4, using all its digits and the basic arithmetic operations.
4096 is the 64-th square number.
It is an amenable number.
It is a practical number, because each smaller number is the sum of distinct divisors of 4096
4096 is an frugal number, since it uses more digits than its factorization.
4096 is an odious number, because the sum of its binary digits is odd.
Multiplying 4096 by its product of nonzero digits (216), we get a cube (884736 = 963).
The spelling of 4096 in words is "four thousand, ninety-six".