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?