Divisor Funtion Inequality: for n > 1, t(n) < 2*sqrt(n)

[patsobi]

I'm trying to show:

for n > 1, t(n) < 2*sqrt(n)

where t(n) is the number of divisors of n. I'm just finding it difficult relating the number of divisors to n itself. Im trying to write n as a product of primes and its divisors also as product of primes but am just getting no where at all... very annoying. Any help/hints would be great.

Also i already know d < sqrt(n) or n/d < sqrt(n), but that hasnt helped either.

 

[pka]

Re: Divisor Funtion Inequality

Have a look at this:
http://mathworld.wolfram.com/DivisorFunction.html