tl;dr
# error on install
n install 8.2.1
mkdir: /usr/local/n/versions/node: Permission denied
mkdir: /usr/local/n/versions/io: Permission denied
# create dir before install
sudo mkdir /usr/local/n
sudo chown -R $(whoami) $_
# then success
n install 8.2.1
Ref: GitHub: Permission denied before running with sudo #416