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A160595
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Numerator of resilience R(n) = eulerphi(n)/(n-1).
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2
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1, 1, 2, 1, 2, 1, 4, 3, 4, 1, 4, 1, 6, 4, 8, 1, 6, 1, 8, 3, 10, 1, 8, 5, 12, 9, 4, 1, 8, 1, 16, 5, 16, 12, 12, 1, 18, 12, 16, 1, 12, 1, 20, 6, 22, 1, 16, 7, 20, 16, 8, 1, 18, 20, 24, 9, 28, 1, 16, 1, 30, 18, 32, 3, 4, 1, 32, 11, 8, 1, 24, 1, 36, 20, 12, 15, 24, 1, 32, 27, 40, 1, 24, 16, 42, 28
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,3
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COMMENTS
| 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
| Project Euler, Problem 245: resilient fractions, May 2009
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EXAMPLE
| a(9)=3 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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MATHEMATICA
| Numerator[Table[EulerPhi[n]/(n - 1), {n, 2, 87}]] (* From Alonso del Arte, Sep 19 2011 *)
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PROG
| (PARI) A160495(n)=numerator(eulerphi(n)/(n-1))
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CROSSREFS
| Sequence in context: A138567 A103530 A090924 * A105778 A088931 A088980
Adjacent sequences: A160592 A160593 A160594 * A160596 A160597 A160598
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KEYWORD
| nonn
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AUTHOR
| M. F. Hasler (www.univ-ag.fr/~mhasler), May 23 2009
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