Search: id:A160599
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%I A160599
%S A160599 15,85,255,259,391,589,1111,3193,4171,4369,12361,17473,21845,25429,
%T A160599 28243,47989,52537,65535,65641,68377,83767,91759,100777,120019,144097,
%U A160599 167743,186367,268321,286357,291919,316171,327937,335923,346063,353029
%N A160599 Composite numbers n for which n-eulerphi(n) divides n-1.
%C A160599 Obviously C(p)=(p-eulerphi(p))/(p-1) = 1/(p-1), i.e. A160598(p)=1, for 
               all primes p. This sequence lists composite numbers for which C(n) 
               has denominator 1, i.e. n-1 is a multiple of n-eulerphi(n).
%C A160599 The sequence contains numbers F(k)*F(k+1)*...*F(k+d), if the factors 
               are successive Fermat primes F(k)=2^(2^k)+1.
%H A160599 Project Euler, <a href="http://projecteuler.net/index.php?section=problems&id=245">
               Problem 245: resilient fractions</a>, May 2009
%e A160599 a(1)=15 is in the sequence, because for n=15, we have (n-eulerphi(n))/
               (n-1) = (15-8)/14 = 1/2; Apart from the primes, this is the smallest 
               number such that C(n) is a unit fraction.
%o A160599 (PARI) for(n=2,10^9, isprime(n) & next; (n-1)%(n-eulerphi(n)) | print1(n",
               "))
%Y A160599 Cf. A160597-A160598.
%Y A160599 Sequence in context: A050405 A020136 A067401 this_sequence A091286 A064058 
               A138322
%Y A160599 Adjacent sequences: A160596 A160597 A160598 this_sequence A160600 A160601 
               A160602
%K A160599 nonn
%O A160599 2,1
%A A160599 M. F. Hasler (MHasler(AT)univ-ag.fr), May 23 2009

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