Hi everybody.

Show that for some positive integer $\displaystyle n$ is composite iff $\displaystyle \sigma(n)>n+\sqrt{n}$.

Thanks.

Printable View

- Apr 10th 2012, 02:46 PMFernandoDivisor summatory function
Hi everybody.

Show that for some positive integer $\displaystyle n$ is composite iff $\displaystyle \sigma(n)>n+\sqrt{n}$.

Thanks. - Apr 10th 2012, 08:53 PMhollywoodRe: Divisor summatory function
Hi Fernando,

Try thinking about what $\displaystyle \sigma(n)$ is when $\displaystyle n$ is not composite (i.e. it is either prime or 1).

- Hollywood - Apr 11th 2012, 02:52 AMFernandoRe: Divisor summatory function
Thanks, the proof is by contradiction, is it not?

Thanks for your suggestion. - Apr 11th 2012, 03:18 AMprincepsRe: Divisor summatory function