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 121
- 121 is the smallest multi-digit palindromic square
- 121 is the sum of the first five powers of 3: 121 = 1 + 3 + 9 + 27 + 81
Rare Properties of 121
The number n is a square if it is the square of an integer.
Common Properties of 121
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.
The n-th lazy caterer number is the maximum number of pieces a (circular) pizza can be cut into with n (straight-line) cuts.
Unlike the situation with cake, everybody gets the toppings.
A number is odd if it is not divisible by 2.
Numbers that are not odd are even. 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.
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.
A composite number is called a Smith number if the sum of its digits equals the sum of all the digits appearing in its prime divisors (counting multiplicity).
In 1984, when Albert Wilansky called his brother-in-law, named Smith, he noticed that the phone number possesses the property described here. Are they called joke numbers, because they were named after an innocent unsuspecting brother-in-law :-) ?
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.