factor/extra/project-euler/072/072.factor

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Factor

! 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-sum ;
! [ euler072 ] 100 ave-time
! 5274 ms ave run time - 102.7 SD (100 trials)
SOLUTION: euler072