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%I #6 Mar 02 2024 13:25:57
%S 6,28,496,6200,8128,33550336,8589869056,137438691328
%N Ore numbers whose nontrivial divisors are not Ore numbers.
%C It seems this is a supersequence of A000396 (confirmed for all available terms of A000396).
%e The nontrivial divisors of 6 are 2 and 3 that do not belong to A001599, so 6 is a term.
%e No nontrivial divisor of 6200 is a term of A001599, which makes 6200 a term of the present sequence. On the other hand, 6200 is not a perfect number.
%t oreQ[n_] := IntegerQ[n*DivisorSigma[0, n]/DivisorSigma[1, n]];
%t ntdNotOreQ[n_] := NoneTrue[Most[Rest[Divisors[n]]], oreQ[#] &];
%t a001599 = Cases[Import["https://oeis.org/A001599/b001599.txt", "Table"],
%t {_, _}][[All, 2]];
%t Select[Rest[a001599], ntdNotOreQ[#] &]
%Y Cf. A000396, A001599.
%K nonn,more
%O 1,1
%A _Ivan N. Ianakiev_, Mar 02 2024