Automorphic number :
An automorphic number is a number which is present in the last digit(s) of its square. Example: 25 is an automorphic number as its square is 625 and 25 is present as the last digits.
A number is said to be a Neon Number if the sum of digits of the square of the number is equal to thenumber itself. Example 9 is a Neon Number. 9*9=81 and 8+1=9.Hence it is a Neon Number.
Magic number :
A number is said to be a Magic number if the sum of its digits are calculated till a single digit is obtained by recursively adding the sum of its digits. If the single digit comes to be 1 then the number is a magic number.
Reverse of a number is also same as the original number.
In mathematics, the nth taxicab number, typically denoted Ta(n) or Taxicab(n), also called the nth Hardy–Ramanujan number, is defined as the smallest number that can be expressed as a sum of two positive cube numbers in n distinct ways. The most famous taxicab number is 1729 = Ta(2) = 13 + 123 = 93 + 103.
A positive integer is called an Armstrong number of order n if abcd… = an + bn + cn + dn + … In case of an Armstrong number of 3 digits, the sum of cubes of each digits is equal to the number itself. For example: 153 = 1*1*1 + 5*5*5 + 3*3*3 // 153 is an Armstrong number.
If the sum of factorial of the digits in any number is equal the given number then the number is called as STRONG number.
Ex=1! +4! +5!= 1+24+120 = 145
Ex: 6 (1,2,3,6 sum of divisors excluding itself=1+2+3=6)
A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).