This one-liner worked at least four different Linux systems with different distros and versions.
echo "USER RSS PROCS" ; echo "-------------------- -------- -----" ; ps hax -o rss,user | awk '{rss[$2]+=$1;procs[$2]+=1;}END{for(user in rss) printf "%-20s %8.0f %5.0f\n", user, rss[user]/1024, procs[user];}' | sort -rnk2
USER RSS PROCS
-------------------- -------- -----
admtest 1974930 11
root 4544 736
gdm 78 12
ntp 14 1
postfix 5 2
messagebus 1 1
uuidd 0 1
