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%I #9 Oct 21 2017 21:52:26
%S 1,4,16,36,144,576,3600,14400,32400,129600,291600,1166400,8643600,
%T 34574400,77792400,84272400,311169600,337089600,700131600,2800526400,
%U 179233689600,202338032400,809352129600
%N Numbers n such that phi(sigma(n))/n > phi(sigma(m))/m for all m < n, where sigma is the sum of divisors function (A000203) and phi is Euler's totient function (A000010).
%C Makowski and Schinzel proved that lim sup phi(sigma(n))/n = oo, thus this sequence is infinite.
%H Andrzej Makowski and Andrzej Schinzel, <a href="http://yadda.icm.edu.pl/yadda/element/bwmeta1.element.bwnjournal-article-cmv13i1n14/c/cm13114.pdf">On the functions phi(n) and sigma(n)</a>, Colloquium Mathematicae, Vol. 13, No. 1 (1964), pp. 95-99.
%t a={}; rm=0; Do[r = EulerPhi[DivisorSigma[1,n]]/n; If[r>rm, rm=r; AppendTo[a,n]], {n,1,100000}]; a
%o (PARI) lista(nn) = {my(rmax = 0); for (n=1, nn, if ((r=eulerphi(sigma(n))/n) > rmax, rmax = r; print1(n, ", ")););} \\ _Michel Marcus_, Oct 18 2017
%Y Cf. A000010, A000203, A062401.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Oct 15 2017
%E a(21)-a(23) from _Robert G. Wilson v_, Oct 16 2017