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Factor Sum

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2
See all short problems arranged by curriculum topic in the short problems collection

Given any positive integer $n$, Paul adds together the distinct factors of $n$, other than $n$ itself.

Which of the numbers $1$, $3$, $5$, $7$ and $9$ can never be Paul's answer?

If you liked this problem, here is an NRICH task that challenges you to use similar mathematical ideas.

This problem is taken from the UKMT Mathematical Challenges.