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

I gave Neel the number of positive divisors of this number and Nitin the sum of positive divisors of this number.

Then the following conversation takes place:

Neel: "I don't know the original number."

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

Neel: "Now I know the original number."

Nitin: "Me too!"

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