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%I #8 Jul 02 2020 16:02:41
%S 1,3,4,5,11,17,23,25,29,59,89,149,179,239,269,359,377,389,419,839,
%T 1049,1259,1889,2099,2309,9239,11549,13859,20789,23099,25409,30029,
%U 90089,180179,210209,270269,300299,330329,390389,420419,540539,570569,1017917,1018013
%N Numbers n such that phi(psi(n))/n < phi(psi(m))/m for all m < n, where phi is Euler's totient function (A000010) and psi is the Dedekind psi function (A001615).
%C Sândor proved that lim inf phi(psi(n))/n = 0, hence this sequence is infinite.
%D Jôzsef Sândor, On Dedekind’s arithmetical function, Seminarul de Teoria Structurilor, Univ. Timisoara, No. 51, 1988, pp. 1-15.
%H Jôzsef Sândor, <a href="https://www.emis.de/journals/JIPAM/article546.html">On the composition of some arithmetic functions, II</a>, Journal of Inequalities in Pure and Applied Mathematics, Vol. 6, Issue 3, Article 73 (2005).
%t psi[n_] := If[n < 1, 0, n*Sum[MoebiusMu[d]^2/d, {d, Divisors@n}]]; a={}; rm=2; Do[r=EulerPhi[psi[n]]/n; If[r<rm, rm=r; AppendTo[a,n]],{n,1,10^5}]; a
%Y Cf. A000010, A001615.
%K nonn
%O 1,2
%A _Amiram Eldar_, Oct 15 2017
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