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A160596 Denominator of resilience R(n) = phi(n)/(n-1).

%I A160596 #20 Sep 08 2022 08:45:45
%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,
%T A160596 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,
%U A160596 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
%N A160596 Denominator of resilience R(n) = phi(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 phi(d) proper fractions among the d-1 possible ones.
%C A160596 a(n) = 1 if and only if n is prime. - _Robert Israel_, Dec 26 2016
%H A160596 Robert Israel, <a href="/A160596/b160596.txt">Table of n, a(n) for n = 2..10000</a>
%H A160596 Project Euler, <a href="http://projecteuler.net/index.php?section=problems&amp;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 canceled 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.
%p A160596 seq(denom(numtheory:-phi(n)/(n-1)),n=2..100); # _Robert Israel_, Dec 26 2016
%t A160596 Denominator[Table[EulerPhi[n]/(n-1),{n,2,90}]] (* _Harvey P. Dale_, Apr 18 2012 *)
%o A160596 (PARI) A160496(n)=denominator(eulerphi(n)/(n-1))
%o A160596 (Magma) [Denominator(EulerPhi(n)/(n-1)): n in [2..80]]; // _Vincenzo Librandi_, Jan 02 2017
%K A160596 nonn,look
%O A160596 2,3
%A A160596 _M. F. Hasler_, May 23 2009