A happy number is defined by the following Sequence: Starting with any
positive integer, replace the number by the sum of the squares of its
digits in base-ten, and repeat the process until the number either equals
1 (where it will stay), or it loops endlessly in a cycle that 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 sad numbers.
For example, 19 is happy, as the associated Sequence is:
- 12 + 92 = 82
- 82 + 22 = 68
- 62 + 82 = 100
- 12 + 02 + 02 = 1.
Print all the happy numbers from 1 to 200 inclusive, each on
their own line.