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%I #14 Jul 30 2023 09:04:17
%S 399,6304359999,408598269695,517270926095,20203946790335
%N Lucas-Carmichael numbers k that have an abundancy index sigma(k)/k that is larger than the abundancy indices of all smaller Lucas-Carmichael numbers.
%C The rounded values of sigma(k)/k are 1.604, 1.612, 1.666, 1.706, 1.752, ...
%C The sequence includes the smallest abundant Lucas-Carmichael number, which is <= 1012591408428327888883952080728349448745451794025524955777432246705535.
%t lc = Import["https://oeis.org/A006972/b006972.txt", "Table"][[;; , 2]]; rm = 0; s = {}; Do[n = lc[[k]]; r = DivisorSigma[-1, n]; If[r > rm, AppendTo[s, n]; rm = r], {k, 1, Length[lc]}]; s
%Y Cf. A000203, A004394, A006972.
%Y Similar sequences: A328691, A329460.
%K nonn,hard,more
%O 1,1
%A _Amiram Eldar_ and _Daniel Suteu_, Aug 29 2022
%E a(5) from _Martin Ehrenstein_, Jul 30 2023