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.