Here is a solution using the lag() function from dplyr.
library(dplyr, warn.conflicts = FALSE)
data <- data.frame(col = c(4, 8, 32, 64))
mutate(data, new_col = col / lag(col))
#> col new_col
#> 1 4 NA
#> 2 8 2
#> 3 32 4
#> 4 64 2
Created on 2020-04-18 by the reprex package (v0.3.0)