Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Unique Properties of 1296
- 1296 is the total number of rectangles one may draw on a standard chessboard
- 1296 is the smallest number with 25 divisors
- 1296 is the smallest square which when subtracted from its reverse forms a positive square
- 1296 is the smallest semiprime to the power of another semiprime (1296 = 94)
Rare Properties of 1296
The number n is a square if it is the square of an integer.
Common Properties of 1296
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
A number is even if it is divisible by 2.
Numbers that are not even are odd. Compare with another pair -- evil and odious numbers.
The number n is odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.
The untouchable numbers are those that are not the sum of the proper divisors of any number.