Is it true that for all positive integers n, the inequality $\displaystyle d(n)\leq 1 + log_2 n$ holds?

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- Aug 17th 2011, 09:48 AMalexmahoneNumber of positive divisors of n
Is it true that for all positive integers n, the inequality $\displaystyle d(n)\leq 1 + log_2 n$ holds?

- Aug 17th 2011, 10:05 AMPlatoRe: Number of positive divisors of n
- Aug 17th 2011, 10:35 AMalexmahoneRe: Number of positive divisors of n
- Aug 17th 2011, 10:56 AMTheChazRe: Number of positive divisors of n
Uh... no!

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... all divide 144, so the left hand side is larger than the right hand side - Aug 17th 2011, 10:58 AMalexmahoneRe: Number of positive divisors of n
- Aug 17th 2011, 10:59 AMPlatoRe: Number of positive divisors of n
- Aug 17th 2011, 11:01 AMalexmahoneRe: Number of positive divisors of n
Perhaps there is a mistake in the book: Is $\displaystyle d(n)\geq 1 + log_2 n$ true?

- Aug 17th 2011, 11:04 AMAlso sprach ZarathustraRe: Number of positive divisors of n