The regular expression:

(?-imsx:(&(?!(?:amp|lt|gt);)|[><]))

matches as follows:

NODE                     EXPLANATION
----------------------------------------------------------------------
(?-imsx:                 group, but do not capture (case-sensitive)
                         (with ^ and $ matching normally) (with . not
                         matching \n) (matching whitespace and #
                         normally):
----------------------------------------------------------------------
  (                        group and capture to \1:
----------------------------------------------------------------------
    &                        '&'
----------------------------------------------------------------------
    (?!                      look ahead to see if there is not:
----------------------------------------------------------------------
      (?:                      group, but do not capture:
----------------------------------------------------------------------
        amp                      'amp'
----------------------------------------------------------------------
       |                        OR
----------------------------------------------------------------------
        lt                       'lt'
----------------------------------------------------------------------
       |                        OR
----------------------------------------------------------------------
        gt                       'gt'
----------------------------------------------------------------------
      )                        end of grouping
----------------------------------------------------------------------
      ;                        ';'
----------------------------------------------------------------------
    )                        end of look-ahead
----------------------------------------------------------------------
   |                        OR
----------------------------------------------------------------------
    [><]                     any character of: '>', '<'
----------------------------------------------------------------------
  )                        end of \1
----------------------------------------------------------------------
)                        end of grouping
----------------------------------------------------------------------