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Write a program that tells whether a given integer is happy. A happy number is found using the following process: Take the sum of the squares of its digits, and continue iterating this process until it yields 1, or produces an infinite loop.

( Hint: http://mathworld.wolfram.com/HappyNumber.html, http://oeis.org/A039943 )

 

For example the number 7:

7^2 = 49

4^2 + 9^2 = 97

9^2 + 7^2 = 130

1^2 + 3^2 + 0^2 = 10

1^2 + 0^2 = 1

 

If a number is not happy than it is obviously unhappy.

Now that you have this program, what is the largest happy number you can find?

What is the happiest number between 1 and 1,000,000.

Defined the happiest number as the smallest number that finds the most other happy numbers with it, i.e. 7 found four other numbers (49, 97, 130, and 10) making it a rank 4 in happiness.