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%I #26 Sep 07 2023 07:14:59
%S 1,5,7,13,31,37,61,181,241,421,899,1321,1333,1763,2161,2521,5183,7561,
%T 12601,15121,28187,30241,55441,110881,167137,278263,332641,555911,
%U 666917,722473,1443853,2165407,3607403,4324321,7212581,8654539,10817761,21631147,36768847
%N Numbers k such that sigma(phi(k))/k > sigma(phi(m))/m for all m < k, where sigma is the sum of divisors function (A000203) and phi is Euler's totient function (A000010).
%C Alaoglu and Erdős proved that lim sup sigma(phi(n))/n = oo, thus this sequence is infinite.
%H Amiram Eldar, <a href="/A293059/b293059.txt">Table of n, a(n) for n = 1..55</a>
%H Leon Alaoglu and Paul Erdős, <a href="https://users.renyi.hu/~p_erdos/1944-01.pdf">A conjecture in elementary number theory</a>, Bulletin of the American Mathematical Society, Vol. 50, No. 12 (1944), pp. 881-882.
%H Florian Luca and Carl Pomerance, <a href="https://eudml.org/doc/283450">On some problems of Makowski-Schinzel and Erdős concerning the arithmetical functions phi and sigma</a>, Colloquium Mathematicae, Vol. 92, No. 1 (2002), pp. 111-130.
%t a={}; rm=0; Do[r = DivisorSigma[1, EulerPhi[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=sigma(eulerphi(n))/n) > rmax, rmax = r; print1(n, ", ")););} \\ _Michel Marcus_, Oct 18 2017
%Y Cf. A000010, A000203, A062402, A067573.
%K nonn
%O 1,2
%A _Amiram Eldar_, Oct 15 2017
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