This investigation is recommended for confident learners. It would probably be better suited to an extra-curricular club than as a whole class activity.

Learners investigate Aliquot sequences which almost always either crash to zero, or go in loops. The exception is the number 276 which even super computers have so far been unable to determine the fate of.

After pupils have investigated it is recommend that you play the linked video.

It is NOT AN INTRODUCTORY VIDEO, but best played to round off the activity.

Divisors and factors.

You may wish to explain what a conjecture is to pupils before they begin. Otherwise pupils can work through the task at their own pace.

It may be sensible to have a few extra questions lined up for pupils that finish early - or perhaps they could investigate Millenium Prize Problems if they have access to a device - before playing the video.