Well I'm going to go under the assumption that you don't have access to things like cron (or at for that matter), as they are usually the tools of choice. Also I'm not sure why you'd want to restrict yourself to 2 date functions that are used primarily for formatting, anyhoo -

use strict;

my $day = (localtime())[3];
while($day < 31) {
    if(0 == $day % 6) {
        do_email_program_thingy();
    } else {
        sleep(60 * 60 * 24);
    }
    $day = (localtime())[3];
}
[download]

This should do something every 6th day, otherwise it just sleeps. This isn't particularly elegant code, or robust for that matter, so I wouldn't recommend a copy'n'paste ;o)
HTH

broquaint