Search: id:A160596
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%I A160596
%S A160596 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,
%T A160596 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,
%U A160596 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
%N A160596 Denominator of resilience R(n) = eulerphi(n)/(n-1).
%C A160596 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.
%H A160596 Project Euler, <a href="http://projecteuler.net/index.php?section=problems&id=245">
               Problem 245: resilient fractions</a>, May 2009
%e A160596 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.
%o A160596 (PARI) A160496(n)=denominator(eulerphi(n)/(n-1))
%Y A160596 Sequence in context: A122383 A136180 A095112 this_sequence A092319 A147410 
               A146623
%Y A160596 Adjacent sequences: A160593 A160594 A160595 this_sequence A160597 A160598 
               A160599
%K A160596 nonn
%O A160596 2,3
%A A160596 M. F. Hasler (MHasler(AT)univ-ag.fr), May 23 2009

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