number of unique elements excluding NA in r

You can use na.omit first:

x <- c(1,2,3,NA,2)
length(unique(na.omit(x)))

Alternatively, n_distinct from dplyr has an na_rm argument:

library(dplyr)
n_distinct(x, na.rm = TRUE)

data.table::uniqueN has na.rm in version v1.9.7+.