Influential is a difficult word. But here goes:
O'Sullivian (the survey aesthetic has been re-appropriated by many contemporary LFCN guys)
Atget (same reason as above)
I've defined 'influential' as those photographers who are clearly visually referenced the most in modern work.
I haven't included Ansel or Weston for the same reason I wouldn't include The Beatles in a music list - goes without saying.