Primo Phobia

Number Theory Level pending

I am thinking of a number which has the following properties:

  1. It is a product of three distinct prime numbers, for which the sum of squares of these 3 numbers is 2331.

  2. There are 7560 positive integer (inclusive of 1) which is less than the number and is coprime to it.

  3. The sum of divisors (inclusive of 1 and itself) is 10560.

What is the number I am thinking of?


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