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 1146
- 1146 is the smallest number such that both the sum of its semiprime divisors and the sum of its prime divisors are squares (The prime divisors 2, 3, and 191 sum to a square 196 = 142. The semiprime divisors 6, 382 and 573 sum to a square 961 = 312.)
Common Properties of 1146
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.
A number is said to be square-free if its prime decomposition contains no repeated factors.
The untouchable numbers are those that are not the sum of the proper divisors of any number.