Eulers's Phi Function
Euler's Phi function (aka Euler's ‘totient’ function).
eulersPhi(n)
n |
Positive integer. |
The phi function is defined to be the number of positive integers
less than or equal to n that are coprime to n, i.e.
have no common factors other than 1.
Natural number, the number of coprime integers <= n.
Works well up to 10^9.
eulersPhi(9973) == 9973 - 1 # for prime numbers
eulersPhi(3^10) == 3^9 * (3 - 1) # for prime powers
eulersPhi(12*35) == eulersPhi(12) * eulersPhi(35) # TRUE if coprime
## Not run:
x <- 1:100; y <- sapply(x, eulersPhi)
plot(1:100, y, type="l", col="blue",
xlab="n", ylab="phi(n)", main="Euler's totient function")
points(1:100, y, col="blue", pch=20)
grid()
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.