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%I #19 Jun 20 2020 03:37:09
%S 1,4,8,16,32,64,72,144,216,288,432,864,1728,2592,3456,3600,5184,7200,
%T 10800,21600,43200,64800,86400,108000,129600,216000,259200,324000,
%U 432000,518400,529200,648000,1058400,2116800,3175200,4233600,5292000,6350400,10584000
%N Numbers n such that sigma(n)/usigma(n) > sigma(m)/usigma(m) for all m < n, where sigma(n) is the sum of divisors of n (A000203) and usigma(n) is the sum of unitary divisors of n (A034448).
%C This sequence is infinite. The smallest values of n for which sigma(n)/usigma(n) > 2, 3 and 4 are a(7), a(19), and a(44).
%H Amiram Eldar, <a href="/A285906/b285906.txt">Table of n, a(n) for n = 1..56</a>
%e sigma(72)=195, usigma(72)=90, and their ratio 195/90=13/6 is higher than sigma(m)/usigma(m) for all m<72, thus 72 is in this sequence.
%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])];
%t a={}; rmax=0; Do[r=DivisorSigma[1, n]/usigma[n]; If[r>rmax, AppendTo[a, n]; rmax=r], {n, 3000}]; a
%Y Cf. A000203, A034448.
%K nonn
%O 1,2
%A _Amiram Eldar_, Apr 28 2017
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