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 168
- 168 is the number of hours in a week
- 168 is the size of the smallest non-cyclic simple group which is not an alternating group
- 168 is the number of primes less than 1000
- 168 is the total number of spots on a set of dominoes (submitted by Ken Knowlton)
- 165 is the smallest number with more than one nonzero digit whose cubed digits sum to a cube (13 + 63 + 83 = 729 = 93)
- 168 is the smallest integer areas of an integer-sided triangle such that the length of its circumradius is a square
Common Properties of 168
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.