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 MAILTO="root" 0 0 * * 1 root /usr/sbin/logwatch