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 1444
- 1444 - smallest pandigital number in Roman numerals - uses all Roman numerals at least once
- 1444 is the smallest start of three consecutive squares the sum of which is equal to the sum of three consecutive primes
Rare Properties of 1444
The number n is a square if it is the square of an integer.
Common Properties of 1444
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.
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.