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 196
- According to conjecture, 196 is the lowest Lychrel number, that is the lowest number which is not known to produce a palindrome by repeated reversal and addition. The algorithm has been tested to more than 246 million digits without finding a palindrome, but no one has ever proven that it will never produce one
- 196 is the smallest square that contains a multidigit prime number as a substring
- 196 is the smallest perfect power which is not coprime to the sum of its divisors
- Web pages about 196:
Rare Properties of 196
The number n is a square if it is the square of an integer.
Common Properties of 196
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 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.