A simple implementation of Euler's totient function ("Phi function"). More info about the function at http://mathworld.wolfram.com/TotientFunction.html. The language used here in this implementation is R (r-base-core 2.15.1-5ubuntu1).

euler_phi.r

# Eulers Totient Function
#
# Description at http://mathworld.wolfram.com/TotientFunction.html
# Algorithm based on http://en.wikipedia.org/wiki/Euler%27s_totient_function
# Interesting property: for a prime number p, epf(p) = p - 1
 
# greatest common divisor of two integers
# @param m int the first number
# @param n int the second number
# @return int the greates common divisor of the two numbers
# inspired by a post at http://mathforum.org/library/drmath/view/51893.html
# <input> M=44305 N=42355
# rem = 1950 (44305 mod 42355)
# rem = 1405 (42355 mod 1950)
# rem =  545 ( 1950 mod 1405)
# ...
# rem =    0 (   10 mod 5)
# <output> 5
gcd <- function (m, n) {
  while (1) {
    rem <- m %% n                         # calculate the remainder here 
    ifelse (rem == 0, break, { m = n; n = rem; }) # if the remainder is greater than 0 then we continue by changing m to the value of n and n to the value of the remainder
  }
  n
}      

# eulers phi function
# @param n int number - the "phi of n"
# @return int the function's value for the given number
epf <- function (n) {
  if (n < 0) { -1 }                       # function's domain are positive integers only
  sum = 0
  for (k in 1:n) {                        # epf(n) is number of positive integers in 1 <= k <= n
    if (gcd(n, k) == 1) { sum = sum + 1 } # for which gcd (n, k) is equal 1. (when gcd (n, k) is 1, the number
  }                                       # k is a totient of n. And epf(n) is the sum of these totients (numbers relatively prime to n)
  sum                                     # return the result
}

# DEMO of epf(n) for a range from 1 to 100
vals <- NULL
for (i in 1:100) {
  vals <- c(vals, epf(i))
}
plot(vals)