39 lines
1.0 KiB
Factor
39 lines
1.0 KiB
Factor
! Copyright (c) 2009 Guillaume Nargeot.
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! See http://factorcode.org/license.txt for BSD license.
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USING: kernel math math.primes.factors math.ranges
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project-euler.common sequences ;
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IN: project-euler.072
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! http://projecteuler.net/index.php?section=problems&id=072
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! DESCRIPTION
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! -----------
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! Consider the fraction, n/d, where n and d are positive integers.
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! If n<d and HCF(n,d)=1, it is called a reduced proper fraction.
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! If we list the set of reduced proper fractions for d ≤ 8 in ascending order
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! of size, we get:
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! 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,
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! 5/7, 3/4, 4/5, 5/6, 6/7, 7/8
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! It can be seen that there are 21 elements in this set.
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! How many elements would be contained in the set of reduced proper fractions
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! for d ≤ 1,000,000?
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! SOLUTION
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! --------
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! The answer can be found by adding totient(n) for 2 ≤ n ≤ 1e6
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: euler072 ( -- answer )
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2 1000000 [a,b] [ totient ] map-sum ;
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! [ euler072 ] 100 ave-time
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! 5274 ms ave run time - 102.7 SD (100 trials)
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SOLUTION: euler072
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