Just change the beginning like this. Today is 14165 days since the epoch, and 14165 % 15 = 5. That means this script will run today, and in 15 days time, 30 days, 45, etc.
Code:
#!/bin/ksh
days_since_epoch=$(perl -e 'print int(time/86400);')
if [[ "$(( $days_since_epoch % 15 ))" -ne 5 ]]
then
exit
fi
...
