Number Gossip
(Enter a number and I'll tell you everything you wanted to know about it but were afraid to ask.)
Common Properties of 8778
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.
A palindrome is a number that reads the same forward or backward.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
A number is said to be square-free if its prime decomposition contains no repeated factors.
If you start with n points on a line, then draw n-1 points above and between, then n-2 above and between them, and so on, you will get a triangle of points. The number of points in this triangle is a triangle number.
Compare to square, pentagonal and tetrahedral numbers.
The untouchable numbers are those that are not the sum of the proper divisors of any number.