I have chosen a positive integer between 5 and 15 inclusive.

I gave Nate the number of positive divisors of this number and Sven the sum of positive divisors of this number.

Then the following conversation takes place:

**Nate:** "I don't know the original number."

**Sven:** "I don't know the original number either."

**Nate:** "Now I know the original number."

**Sven:** "Me too!"

Assuming that they both are perfectly logical and are always telling the truth, what was the original number?

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