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%I #35 Nov 22 2016 21:44:53
%S 561,1105,2821,6601,10585,29341,52633,62745,63973,101101,115921,
%T 126217,188461,252601,278545,294409,410041,512461,552721,748657,
%U 825265,1152271,1193221,2100901,2508013,2531845,3146221,4335241,4767841,4909177,5444489,5481451,6049681
%N Composite numbers n such that gcd(phi(n), n-1) = lambda(n), where lambda(n) = A002322(n).
%C Carmichael numbers n such that A049559(n) = A002322(n).
%C If n is a Carmichael number with n-1 squarefree, then n is in the sequence. The smallest such n = 139952671.
%C If (n-1)/lambda(n) is a prime (see A174590), then n is in the sequence. - _Thomas Ordowski_, Oct 17 2016
%C Numbers n such that gcd(phi(n),n-1) = lambda(n)^2 are 1, 2, 2320690177, ? - _Thomas Ordowski_ and _Michel Marcus_, Oct 20 2016
%H Robert Israel, <a href="/A264012/b264012.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[ Range@ 6100000, CompositeQ@# && GCD[ EulerPhi@#, # - 1] == CarmichaelLambda@# &] (* _Michael De Vlieger_, Nov 01 2015 *)
%o (PARI) forcomposite(n=1, 1e7, if(gcd(eulerphi(n),n-1)==lcm(znstar(n)[2]), print1(n ", "))) \\ _Altug Alkan_, Nov 01 2015
%o (PARI) t(n)=my(f=factor(n)); for(i=1, #f[, 1], if(f[i, 2]>1||(n-1)%(f[i, 1]-1), return(0))); 1;
%o is(n)=n%2 && !isprime(n) && t(n) && n>1;
%o c(n)=gcd(eulerphi(n),n-1)/lcm(znstar(n)[2]);
%o for(n=1, 1e7, if(is(n) && c(n)==1 , print1(n", "))) \\ _Altug Alkan_, Nov 01 2015
%Y Cf. A002322, A002997, A049559, A257643.
%K nonn
%O 1,1
%A _Thomas Ordowski_, Nov 01 2015
%E More terms from _Altug Alkan_, Nov 01 2015