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 2401
- 2401 is the smallest number (except 1) that is the 4th power of the sum of its digits
- 2401 is the smallest fourth power that becomes prime when its leftmost digit is removed
- 2401 is the largest number that equals the sum of its digits to the power of the number of its digits
- 2401 is the smallest 4-digit number that is a power of the sum of its digits
Rare Properties of 2401
The number n is a square if it is the square of an integer.
Common Properties of 2401
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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 odd if it is not divisible by 2.
Numbers that are not odd are even. 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.
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.