Let S(n) be the sum of the divisors of a positive integer n. This includes both 1 and n itself. For example, S(6) = 12.
Find all solutions to the equation:
S(n + 2) = S(n) + 2
where 0 < n < 100
Remember that these questions should be done by hand and without a calculator!
The art of solving such questions is to quickly find some pattern or underlying structure so that you do not have to calculate S(n) for all values of n.
As always, the top prize requires a full solution and a brief method of the steps taken.
Any questions, just ask!
image: designed myself
The Prizes
Earnings from each Brainsteem Puzzle will go towards the next Prizes.
For this Brainsteem # 5 the Prizes are:
2 SBD for the first correct answer that includes a valid method
1 SBD for one other correct answer that will be chosen randomly. That means you can still win this prize even if the answer may already be visible!
Please upvote! Resteem if you think this is a great puzzle! I will upvote all correct answers and any other interesting comments. To be fair to everyone, the prize closes after 7 days. Winners will be notified after that date and usernames posted with a solution.
Enjoy!