PDF file. We frequently awake during the night wondering about mathemagical alakazams. Sometimes we leap out of bed and jot down notes to remind us to check out an idea. One night we woke in the wee hours wondering about products of proper factors of natural numbers. We eased out of bed and wrote a note to look it up on the Internet. Later that day, we cranked up our computer and searched for
products of proper factors
We found zilch, nada, nothing about products of proper factors of numbers. We did another search:
sums of proper factors [12 million hits!]
On the Internet, there is much ado about sums of proper factors of natural numbers, but we did not find anything about products of proper factors of natural numbers.
Aha! Is this unexplored territory? (We don't know.) In this 52-page eBook, we explore products of proper factors. We leave much exploring undone and hope that YOU and YOUR STUDENTS will continue the exploration.