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A067793 Nonprimes n such that phi(n) > 2n/3.

%I A067793 #47 Sep 08 2022 08:45:05
%S A067793 1,25,35,49,55,65,77,85,91,95,115,119,121,125,133,143,145,155,161,169,
%T A067793 175,185,187,203,205,209,215,217,221,235,245,247,253,259,265,275,287,
%U A067793 289,295,299,301,305,319,323,325,329,335,341,343,355,361,365,371,377,391,395,403,407,413,415,425,427
%N A067793 Nonprimes n such that phi(n) > 2n/3.
%C A067793 Differs from A038509 in the first entry and in addition as documented in A069043. - _R. J. Mathar_, Sep 30 2008
%C A067793 It appears that a(n) lists the composite values of n which satisfy the condition sum(k^2,k=1..n) mod n = A000330(n) mod n = A215573(n) = 0. - _Gary Detlefs_, Nov 16 2011
%C A067793 Conjecture: Odd composite n such that (n^2 + 8) mod 3 = 0. (All primes > 3 meet this criterion). - _Gary Detlefs_, May 03 2012
%C A067793 Both conjectures are wrong.  The first counterexample is 385. - _Robert Israel_, May 17 2017
%C A067793 The semiprime numbers p * q, p, q > 3, are terms. - _Marius A. Burtea_, Oct 01 2019
%H A067793 Robert Israel, <a href="/A067793/b067793.txt">Table of n, a(n) for n = 1..10000</a>
%e A067793 10 is not in the list because phi(10) = 4 < 2*10/3. 25 is in the list because phi(25) = 20 > 2*25/3.
%p A067793 select(n -> not isprime(n) and numtheory:-phi(n) > 2*n/3, [$1..1000]); # _Robert Israel_, May 17 2017
%t A067793 Select[Range[1000], ! PrimeQ[#] && EulerPhi[#] > 2 #/3 &] (* _T. D. Noe_, Nov 02 2011 *)
%o A067793 (PARI) lista(nn) = {for (n=1, nn, if (!isprime(n) && (eulerphi(n)/n > 2/3), print1(n, ", ")););} \\ _Michel Marcus_, Jul 05 2015
%o A067793 (Magma) [k:k in [1..400]| not IsPrime(k) and EulerPhi(k) gt 2*k/3]; // _Marius A. Burtea_, Oct 01 2019
%Y A067793 Cf. A166362.
%K A067793 nonn
%O A067793 1,2
%A A067793 _Benoit Cloitre_, Feb 07 2002
%E A067793 Definition clarified by _Michel Marcus_, Jul 05 2015
%E A067793 Incorrect Maple program removed by _Robert Israel_, May 17 2017