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%I #15 Aug 23 2017 11:20:05
%S 1,2,5,18,164,1538,20018,408404,7759748,148728578,6976017044,
%T 7317446132
%N Numbers n such that usigma(usigma(n))/usigma(n) > usigma(usigma(m))/usigma(m) for all m < n, where usigma(n) is the sum of unitary divisors of n (A034448).
%C The unitary version of A289124.
%H Paul Erdős and M. V. Subbarao, <a href="http://www.math.ualberta.ca/~subbarao/documents/Subbarao1.pdf">On the iterates of some arithmetic functions</a>, The theory of arithmetic functions (Proc. Conf., Western Michigan Univ., Kalamazoo, Mich. 1971), Lecture Notes in Math., 251 , pp. 119-125, Springer, Berlin, 1972. [<a href="http://www.renyi.hu/~p_erdos/1972-17.pdf">alternate link</a>]
%t usigma[n_] := If[n == 1, 1, Times @@ (1 + Power @@@ FactorInteger[n])]; a = {}; k=1; rmax = 0; While[Length[a]<8, s = usigma[ k]; s2 = usigma[ s]; r = s2/s; If[r > rmax, AppendTo[a, k]; rmax = r]; k++]; a
%Y Cf. A034448, A055033, A289124.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Jun 25 2017
%E a(10)-a(12) from _Giovanni Resta_, Aug 23 2017