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 2688
- 2688 is the only 4-digit number in which the sum of digits is equal to the sum of prime factors: 2688 = 2 * 2 * 2 * 2 * 2 * 2 * 2 * 3 * 7 and 2 + 6 + 8 + 8 = 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 + 7)
Common Properties of 2688
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 odious if it has an odd number of 1's in its binary expansion.
Guess what evil numbers are.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
A composite number is called a Smith number if the sum of its digits equals the sum of all the digits appearing in its prime divisors (counting multiplicity).
In 1984, when Albert Wilansky called his brother-in-law, named Smith, he noticed that the phone number possesses the property described here. Are they called joke numbers, because they were named after an innocent unsuspecting brother-in-law :-) ?