--- /dev/null
+! Copyright (c) 2009 Guillaume Nargeot.
+! See http://factorcode.org/license.txt for BSD license.
+USING: kernel math math.primes.factors math.ranges
+project-euler.common sequences ;
+IN: project-euler.072
+
+! http://projecteuler.net/index.php?section=problems&id=072
+
+! DESCRIPTION
+! -----------
+
+! Consider the fraction, n/d, where n and d are positive integers.
+! If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
+
+! If we list the set of reduced proper fractions for d ≤ 8 in ascending order
+! of size, we get:
+
+! 1/8, 1/7, 1/6, 1/5, 1/4, 2/7, 1/3, 3/8, 2/5, 3/7, 1/2, 4/7, 3/5, 5/8, 2/3,
+! 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
+
+! It can be seen that there are 21 elements in this set.
+
+! How many elements would be contained in the set of reduced proper fractions
+! for d ≤ 1,000,000?
+
+
+! SOLUTION
+! --------
+
+! The answer can be found by adding totient(n) for 2 ≤ n ≤ 1e6
+
+: euler072 ( -- answer )
+ 2 1000000 [a,b] [ totient ] [ + ] map-reduce ;
+
+! [ euler072 ] 100 ave-time
+! 5274 ms ave run time - 102.7 SD (100 trials)
+
+SOLUTION: euler072
project-euler.049 project-euler.052 project-euler.053 project-euler.054
project-euler.055 project-euler.056 project-euler.057 project-euler.058
project-euler.059 project-euler.063 project-euler.067 project-euler.069
- project-euler.071 project-euler.073 project-euler.075 project-euler.076
- project-euler.079 project-euler.085 project-euler.092 project-euler.097
- project-euler.099 project-euler.100 project-euler.102 project-euler.112
- project-euler.116 project-euler.117 project-euler.124 project-euler.134
- project-euler.148 project-euler.150 project-euler.151 project-euler.164
- project-euler.169 project-euler.173 project-euler.175 project-euler.186
- project-euler.190 project-euler.203 project-euler.215 ;
+ project-euler.071 project-euler.072 project-euler.073 project-euler.075
+ project-euler.076 project-euler.079 project-euler.085 project-euler.092
+ project-euler.097 project-euler.099 project-euler.100 project-euler.102
+ project-euler.112 project-euler.116 project-euler.117 project-euler.124
+ project-euler.134 project-euler.148 project-euler.150 project-euler.151
+ project-euler.164 project-euler.169 project-euler.173 project-euler.175
+ project-euler.186 project-euler.190 project-euler.203 project-euler.215 ;
IN: project-euler
<PRIVATE