Logwatch can be set up to send weekly server reports.

First, set up a local mail relay and aliases to send root mail to your mailbox.


sudo apt install logwatch


Set up weekly report

LogDir = /var/log
TmpDir = /var/cache/logwatch
Output = mail
Format = text
Encode = none
MailTo = root
MailFrom = Logwatch
Archives = Yes
Range = between -7 days and -1 days
Detail = Low
Service = All
Service = "-zz-network"
Service = "-zz-sys"
Service = "-eximstats"
mailer = "/usr/sbin/sendmail -t"

Then, delete the default daily script:

sudo rm -v /etc/cron.daily/00logwatch

And create a weekly cron task

sudo vim /etc/cron.d/logwatch
# Run weekly - Monday at midnight
0 0 * * 1   root    /usr/sbin/logwatch