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 676
- 676 is the smallest palindromic square whose square root is not palindromic
- 676 is the smallest number whose sum of squarefree divisors and sum of nonsquarefree divisors are both squarefree numbers
- 676 is the smallest palindrome whose product of digits is a non-trivial palindrome
Rare Properties of 676
The number n is a square if it is the square of an integer.
Common Properties of 676
A positive integer greater than 1 that is not prime is called composite.
Composite numbers are opposite to prime numbers.
The number n is deficient if the sum of all its positive divisors except itself is less than n.
Compare with perfect and abundant 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 evil if it has an even number of 1's in its binary expansion.
Guess what odious numbers are.
A palindrome is a number that reads the same forward or backward.
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.
Undulating numbers are numbers of the form abababab... in base 10.
This property is significant starting from 3-digit numbers, so we will not consider numbers below 100.