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 768
- 768 is the smallest number n such that n times n+1 gives the concatenation of two numbers m and m+2 (768*769 = 590592)
- 768 is the number of distinct Hadamard matrices of order 4
- 768 is the smallest area of a cyclic quadrilateral PQRS with non-increasing sequence of sides PQ, QR, RS, and SP, such that the area, the sides, the radius of the circumcircle, and the two diagonals are integers
Common Properties of 768
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.
The untouchable numbers are those that are not the sum of the proper divisors of any number.