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Search: id:A160596
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| A160596 |
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Denominator of resilience R(n) = eulerphi(n)/(n-1). |
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+0
1
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| 1, 1, 3, 1, 5, 1, 7, 4, 9, 1, 11, 1, 13, 7, 15, 1, 17, 1, 19, 5, 21, 1, 23, 6, 25, 13, 9, 1, 29, 1, 31, 8, 33, 17, 35, 1, 37, 19, 39, 1, 41, 1, 43, 11, 45, 1, 47, 8, 49, 25, 17, 1, 53, 27, 55, 14, 57, 1, 59, 1, 61, 31, 63, 4, 13, 1, 67, 17, 23, 1, 71, 1, 73, 37, 25, 19, 77, 1, 79, 40, 81, 1
(list; graph; listen)
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OFFSET
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2,3
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COMMENT
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The resilience of a denominator, R(d), is the ratio of proper fractions n/d, 0<n<d, that are resilient, i.e., such that gcd(n,d)=1. Obviously this is the case for eulerphi(d) proper fractions among the d-1 possible ones.
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LINKS
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Project Euler, Problem 245: resilient fractions, May 2009
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EXAMPLE
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a(9)=4 since for the denominator d=9, among the 8 proper fractions n/9 (n=1,...,8), six cannot be cancelled down by a common factor (namely 1/9, 2/9, 4/9, 5/9, 7/9, 8/9), thus R(9) = 6/8 = 3/4.
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PROGRAM
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(PARI) A160496(n)=denominator(eulerphi(n)/(n-1))
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CROSSREFS
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Sequence in context: A122383 A136180 A095112 this_sequence A092319 A147410 A146623
Adjacent sequences: A160593 A160594 A160595 this_sequence A160597 A160598 A160599
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler (MHasler(AT)univ-ag.fr), May 23 2009
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