For information on properties of a number enter your number into this Number Gossip site from Tanya Khovanova.
Looking at the various properties given we see that one property given is whether a number is happy. Happy Numbers makes a great investigation for students – they see the value in being systematic and recording their findings carefully as careful recording can save them much work as they develop the investigation. (The Happy Numbers starter above comes the Starter of the Day site. from Transum Software.)