Number of Positive Divisors
If d(n) denotes the number of divisors (+ve) of integer n. Prove that .
So, we are not told if n is prime or composite, so I don't know how to approach this proble. But if we suppose the prime factorization of n is ,
then number of divisors of n are: .
So, how do I show that ?
I also know that if n is composite then the number of its divisors are less than or equal to (the notation means the integer part of ), but I don't know if that helps at all.
Any helps is really appreciated.