A297364 - OEIS

A297364

Numbers k such that f(k) > f(m) for all m < k, where f(k) = usigma(usigma(usigma(k)))/usigma(usigma(k)) and usigma(k) is the sum of unitary divisors of k (A034448).

%I #14 Sep 08 2021 21:17:30

%S 1,2,4,10,138,163,2511,36943,408403,9869857,11051023

%N Numbers k such that f(k) > f(m) for all m < k, where f(k) = usigma(usigma(usigma(k)))/usigma(usigma(k)) and usigma(k) is the sum of unitary divisors of k (A034448).

%C 1

%H Imre Kátai and M. Wijsmuller, <a href="http://dx.doi.org/10.1023/A:1006518124057">On the iterates of the sum of unitary divisors</a>, Acta Mathematica Hungarica, Vol 79, No. 1-2 (1998), pp. 149-167.

%t usigma[n_] := Block[{d = Divisors[n]}, Plus @@ Select[d, GCD[ #, n/# ] == 1 &]]; a = {}; k=1; rmax = 0; While[Length[a]<10, s = usigma[ k];s1=usigma[s]; s2 = usigma[ s1]; r = s2/s1; If[r > rmax, a = AppendTo[a, k]; rmax = r]; k++]; a

%Y Cf. A034448.

%K nonn,more

%O 1,2

%A _Amiram Eldar_, Dec 29 2017

%E a(10) and a(11) from _Robert G. Wilson v_, Jan 12 2018