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

),

This is false: 36 has 9 positive divisors, and . What did you __really__ mean here?

Tonio
but I don't know if that helps at all.

Any helps is really appreciated.