The chazzan says “Borchu…” loud enough for all to hear. All respond “Boruch Hashem ham’vorach…” even if some didn’t hear the chazzan. Then the chazzan also says “Boruch Hashem ham’vorach…” and no omayn response is necessary. (ShA1 – MB1,2,4)
If you came late to shul only to hear the chazzan’s “Boruch Hashem ham’vorach…”, do not say it with him – just answer omayn after his words. (MB 1)
If you didn’t hear the chazzan say “Borchu…” don’t answer “Boruch Hashem…” with those (less than 9 people) who heard him. Rather, say omayn after their response. But if 9 people heard the chazzan, you may respond “Boruch Hashem…” with everyone else. (BeH “v’onim”)
You should be silent and concentrate on the chazzan’s “Borchu”. (MB5)