# 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 44

- 44 is the smallest number which is the sum of a reversible pair of non-palindromic primes, 13 + 31
- 44 is the first number such that it and the next number are the product of a prime and another distinct prime squared (44 = 2
^{2}*11 and 45 = 3^{2}*5)
- 44 is the smallest side of the smallest Euler brick
- There are 44 derangements of 5 objects

## Common Properties of 44

A positive integer greater than 1 that is not prime is called *composite*.

Composite numbers are opposite to prime numbers.

The number n is *deficient* if the sum of all its positive divisors except itself is less than n.

Compare with perfect and abundant 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.

One can take the sum of the squares of the digits of a number. Those numbers are *happy* for which iterating this operation eventually leads to 1.

The number n is *odious* if it has an odd number of 1's in its binary expansion.

Guess what evil numbers are.

A *palindrome* is a number that reads the same forward or backward.