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 264
- 264 is the largest known number whose square is undulating: 2642 = 69696
- 264 is the smallest multidigit number that is the sum of its digit into the first or fourth power (264 = 21 + 61 + 44)
Common Properties of 264
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.
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.