SPECIAL TYPES OF NUMBERS

1] PALINDROME NUMBERS

A palindromic number is a number that is the same when written forwards or backwards, i.e., of the form . 

For example numbers like 121,4004,66..etc

2]  ARMSTRONG NUMBERS

An Armstrong number of three digits is an integer such that the sum of the cubes of its digits is equal to the number itself. 

For example, 371 is an Armstrong number since 3³ + 7³ + 1³ = 371.

3] AUTOMORPHIC NUMBERS

In mathematics an automorphic number is a number whose square "ends" in the same digits as the number itself.

For example, 5² = 25, 6² = 36, 26² = 676,  35² = 1225...etc


4] NEON NUMBERS

A number is said to be a Neon Number if the sum of digits of the square of the number is equal to the number itself. 

For Example 9 is a Neon Number. 9*9=81 and 8+1=9.Hence it is a Neon Number.

5] AMICABLE NUMBERS

Amicable numbers are a pair of numbers with the following property: the sum of all of the proper divisors of the first number (not including itself) exactly equals the second number while the sum of all of the proper divisors of the second number (not including itself) likewise equals the first number.

For example let's show that 220 & 284 are amicable numbers:
First we find the proper divisors of 220:
1, 2, 4, 5, 10, 11, 20, 22, 44, 55, 110
If you add up all of these numbers you will see that they sum to 284.
Now find the proper divisors of 284:
1, 2, 4, 71, 142
These sum to 220, and therefore 220 & 284 are amicable numbers.