# 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 26

- 26 is the only natural number to be sandwiched between a square and a cube. Even stronger, 26 is the only number to be sandwiched between any two non-trivial powers
- 26 is the smallest non-palindrome with a palindromic square
- 26 is the number of sporadic finite simple groups (submitted by Paton J. Lewis)
- 26 is the smallest semiprime sandwiched between two not squarefree numbers (submitted by Massimo Kofler)
- 26 is the smallest positive number that is one less than a cube, while the sum of digits is a cube

## Rare Properties of 26

The n-th *cake* number is the maximum number of pieces a (cylindrical) cake can be cut into with n (straight-plane) cuts.

Unfortunately, not everybody gets the frosting. If you cut pizza rather than cake, you get lazy caterer's numbers.

## Common Properties of 26

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.

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

Guess what evil numbers are.

A number is said to be *square-free* if its prime decomposition contains no repeated factors.

The next *Ulam* number is uniquely the sum of two earlier distinct Ulam numbers.