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 288
- 288 is the number of completed Sudokus of size 4 by 4
- 288 is the smallest non-palindrome non-square without trailing zeros such that when multiplied by its reverse is a square: 288 * 882 = 5042
- 288 = 11 + 22 + 33 + 44
- 288 is the product of the first four factorials
- 288 is the smallest number that is a member of an amicable pair where only abundant aliquot parts are considered: (288 is paired with 450)
Common Properties of 288
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.
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.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
The untouchable numbers are those that are not the sum of the proper divisors of any number.