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 2500
- The diagonals of a regular heptadecagon divide it into 2500 regions
- 2500 is the smallest number n whose distinct prime factors are exactly the same as the distinct prime factors of each of the numbers obtained by deleting any single digit of n
Rare Properties of 2500
The number n is a square if it is the square of an integer.
Common Properties of 2500
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.
An integer n is powerful if for every prime p dividing n, p2 also divides n.
How much power? They all can be written as a2 b3.
The number n is practical if all numbers strictly less than n are sums of distinct divisors of n.
The untouchable numbers are those that are not the sum of the proper divisors of any number.