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Numbers n such that psi(phi(n))/n > psi(phi(m))/m for all m < n, where phi is Euler's totient function (A000010) and psi is the Dedekind psi function (A001615).
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%I #8 Jul 02 2020 16:02:32

%S 1,5,7,13,19,31,61,151,181,211,421,631,1051,1471,2311,4621,9241,11551,

%T 18481,25411,32341,34651,43891,60653,120121,150151,180181,270271,

%U 300301,330331,390391,420421,450451,540541,600601,660661,840841,870871,1023053,2045003

%N Numbers n such that psi(phi(n))/n > psi(phi(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 sup psi(phi(n))/n = oo, 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=0; Do[r=psi[EulerPhi[n]]/n; If[r>rm, rm=r; AppendTo[a,n]],{n,1,100000}]; a

%Y Cf. A000010, A001615.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 15 2017