(*This Program is designed to generate the order of the Haros-Farey Sequence (widely known as the Farey Sequence) whose argument is Fibonacci(n + 1); Farey(m) where m = Fibonacci (n + 1), using the using the Euler's Totient Function.  Fibonacci(n + 1) is the Sequence A000045: 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, ....  Farey(Fibonacci(n + 1)) is the Sequence A176499: 2, 3, 5, 11, 23, 59, 141, 361, 941, 2457, 6331, 16619, 43359, 113159, 296385, 775897, 2030103, 5315385, 13912615, 36421835, 95355147, 249635525, 653525857, 1710966825, 4479358275, ...  Start the Program by entering the value of n.  Example: n = 5, m = Fibonacci(6) = 8, Farey(8) = 23.  These sequences occur in the upper bound of networks formed by n equal resistors.  Author: Sameen Ahmed KHAN, rohelakhan@yahoo.com, http://SameenAhmedKhan.webs.com/ and http://sites.google.com/site/rohelakhan/ E-Print archive: http://arxiv.org/abs/1004.3346/ (21 April 2010) Date: Wednesday the 21 April 2010*)

n = 5; 
m = Fibonacci[n + 1];
FareyFibonacci = 1 + Sum[EulerPhi[i], {i, 0, m}];
Print[StringForm["n = ``, m = Fibonacci(n + 1) = ``, Order of Farey Fibonacci Set = ``, CPU time in seconds = ``", n, m, FareyFibonacci, TimeUsed[%] ]]