#Perl, <strike>23</strike> 20 bytes

    say/^(?!(..+)\1+$)/

using <code>-n</code> option.

<strike>
    say<>=~/^(?!(..+)\1+$)/
</strike>

Using the regular expression+unary input approach, prints <code>11</code> (or whatever number you entered) or a blank line.

**Bonus:** decimal version, 31 bytes

    (1x<>)=~/^1$|^(11+)\1+$/||say 1