Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n). If d(a) = b and d(b) = a, where a != b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000.
My first attempt was using for-loop, the code is hard to read and slow. So I switch to vectorized and functional methods which turns out to be cleaner and speedier.
d <- function(n) {
if (n %in% c(0, 1)) return(0)
sum((1:n)[n %% 1:n == 0]) - n
}
is_amicable <- function(n) n == d(d(n)) & n != d(n)
ami_nums <- Filter(is_amicable, 1:9999)
sum(ami_nums)## [1] 31626