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 220
- 220 is the smallest amicable number
- The diagonals of a regular decagon divide it into 220 regions
Rare Properties of 220
The number n is amicable if it belongs to an amicable pair. Two numbers n and m are called an amicable pair if the sum of all positive divisors of n is equal to the sum of all positive divisors of m and both are equal to n + m.
It all started with perfect numbers which are amicable with themselves. Those numbers adopted social virtues and qualities; for the parts of each of them have the power to generate the other. See also sociable numbers.
A tetrahedral number is the number of balls you can put in a triangular pyramid.
This is the space generalization of triangular and square numbers.
Common Properties of 220
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.
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.