Haskell, 33 bytes
(a#b)x=sum[1|0<-mod<$>[a..b]<*>x] Explanation:
(a#b)x --take two values a and b and the list x [a..b] --generate the range a, a+1, ... , b mod<$>[a..b] --partially apply "mod" to each entry of the list mod<$>[a..b]<*>x --apply the partially applied functions to all values of the list x [1|0<-mod<$>[a..b]<*>x] --generate a new list with a one for every zero in the resultingpreviously computed list (a#b)x=sum[1|0<-mod<$>[a..b]<*>x] --sum it all up