A370789 - OEIS

%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