Ask HN: Why would a botnet access my server like that?

My website gets a lot of 'traffic' from seemingly random ips, all requesting the same (broken) url. It seems I have been targeted by a botnet, but I don't understand the goal of those requests: they are clearly not trying to attack, and not fast enough to be a DDOS.

I get on average one of those requests every couple of seconds. This has been going on for more than a year now. Any idea what those are?

Here is an example from my log (ip and server name redacted):

xxx.xxx.xxx.xxx myserver.com - [13/Sep/2016:06:34:49 +0200] "GET /invalid HTTP/1.1" 403 345 "-" "Mozilla/5.0" xxx.xxx.xxx.xxx myserver.com - [13/Sep/2016:06:35:10 +0200] "GET /invalid HTTP/1.1" 403 345 "-" "Mozilla/5.0"