Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Rare Properties of 9120
The number is called pronic if it is the product of two consecutive numbers.
They are twice triangular numbers.
Common Properties of 9120
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.
The number n is called an apocalyptic power if 2n contains the consecutive digits 666 (in decimal).
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.
One can take the sum of the squares of the digits of a number. Those numbers are happy for which iterating this operation eventually leads to 1.
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.
The next Ulam number is uniquely the sum of two earlier distinct Ulam numbers.
The untouchable numbers are those that are not the sum of the proper divisors of any number.