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 254
- 254 is the smallest composite number all of whose divisors (except 1) contain the digit 2
- 254 is the smallest number that is a concatenation of two numbers i and j such that n equals the sum of i-th and j-th prime numbers (2-nd and 54-th prime numbers are 3 and 251, which sum up to 254)
Common Properties of 254
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 n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.
Unlike the situation with cake, everybody gets the toppings.
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.