var+= adds string instead of sum - shell

Question

I have to make a script that makes the sum of all processes that have PIDS greater than 20. It kind of works but something is going wrong. I know it's something simple, base thing, but I can't get the logic.
For example I have 2 processes, "1504" and "1405". My result of sum is 15041405. How do I have to re-write sum+=${proc[$i]} to make an actual sum, not string attach?
proc=( $(ps | cut -d ' ' -f1) )
nr=$(ps | cut -d ' ' -f1 | wc -l)
sum=0
for (( i=0 ; i<=nr ; i++)); do
[[ ${proc[$i]} -gt 20 ]] && sum+=${proc[$i]}
done
echo $sum

Answer 1

Use a math context. In POSIX sh:
sum=$(( sum + val ))
...or, also valid POSIX:
: "$(( sum += val ))"
...or, in bash:
(( sum += val ))
You can also use much easier-to-read comparison operations in a math context, rather than using -gt inside of a non-math test context. In bash:
(( ${proc[$i]} >= 20 )) && (( sum += ${proc[$i]} ))
...or in POSIX shell (which doesn't support arrays, and so cannot exactly reproduce your sample code):
: "$(( sum += ( val < 20 ) ? 0 : val ))"
If you were trying to do the (more sensible) operation of counting PIDs, I'd consider an implementation more like the following (bash-only and Linux-only, but considerably more efficient):
count=0
for pid_file in /proc/[0-9]*; do
pid=${pid_file##*/}
(( pid > 20 )) && (( count++ ))
done
printf '%s\n' "$count"
...or, to put more of the effort on the glob engine:
# avoid inflating the result with non-matching globs
shopt -s nullglob
# define a function to avoid overwriting the global "$#" array
count_procs() {
set -- /proc/[3-9][0-9] /proc/[0-9][0-9][0-9]*
echo "$#"
}
# ...used as follows:
count_procs