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%I #12 Mar 14 2021 05:14:42
%S 2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,20,21,24,28,30,32,33,35,36,39,
%T 40,42,44,45,48,51,52,55,56,57,60,63,91,117,126,133,171,182,189,217,
%U 234,247,252,259,266,273,275,279,341,451,550,671,682,775,781,825,902
%N Number k > 1 such that gpf(phi(k)/lambda(k)) = A006530(A000010(k)/A002322(k)) > log(log(k))^2.
%C The asymptotic density of this sequence is 0 (Erdős et al., 1991).
%C Since log(log(k))^2 > 1 for k >= 16, the only terms of A033948 (numbers k such that phi(k) = lambda(k)) in this sequence are those below 16.
%D József Sándor and Borislav Crstici, Handbook of Number theory II, Kluwer Academic Publishers, 2004, Chapter 3, p. 194.
%H Amiram Eldar, <a href="/A342478/b342478.txt">Table of n, a(n) for n = 1..10000</a>
%H Paul Erdős, Carl Pomerance and Eric Schmutz, <a href="https://eudml.org/doc/206359">Carmichael's lambda function</a>, Acta Arithmetica 58 (1991), pp. 363-385; <a href="http://www.math.dartmouth.edu/~carlp/PDF/lambda.pdf">alternative link</a>.
%t p[n_] := FactorInteger[n][[-1, 1]]; q[n_] := p[EulerPhi[n]/CarmichaelLambda[n]] / Log[Log[n]]^2 > 1; Select[Range[1000], q]
%Y Cf. A000010, A002322, A006530, A033948, A034380.
%K nonn
%O 1,1
%A _Amiram Eldar_, Mar 13 2021