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 8208
- 8208 is the only 4-digit number that equals the fourth power of its first digit plus the fourth power of the second digit plus the fourth power of the last two-digit number: 8208 = 84 + 24 + 84
Rare Properties of 8208
A k-digit number n is called narcissistic if it is equal to the sum of k-th powers of its digits. They are also called Plus Perfect numbers.
Common Properties of 8208
The number n is abundant if the sum of all its positive divisors except itself is more than n.
They are abundant above perfection, not to mention deficiency. See perfect and deficient numbers.
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.
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 evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.